diff --git a/chapter5.ipynb b/chapter5.ipynb
index cdb9a03..389b82b 100644
--- a/chapter5.ipynb
+++ b/chapter5.ipynb
@@ -6,12 +6,12 @@
    "metadata": {
     "collapsed": true,
     "ExecuteTime": {
-     "end_time": "2026-03-22T08:08:29.467878519Z",
-     "start_time": "2026-03-22T08:08:28.169276694Z"
+     "end_time": "2026-03-25T12:53:19.596857715Z",
+     "start_time": "2026-03-25T12:53:16.588300896Z"
     }
    },
    "source": [
-    "import d2l\n",
+    "\n",
     "import torch\n",
     "import d2l\n",
     "import numpy\n",
@@ -24,8 +24,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-03-22T08:08:29.562521238Z",
-     "start_time": "2026-03-22T08:08:29.470022979Z"
+     "end_time": "2026-03-25T12:53:19.882978594Z",
+     "start_time": "2026-03-25T12:53:19.641379604Z"
     }
    },
    "cell_type": "code",
@@ -39,10 +39,10 @@
     {
      "data": {
       "text/plain": [
-       "tensor([[ 0.0362,  0.0737, -0.0211,  0.0666, -0.1115,  0.0158, -0.1162,  0.0884,\n",
-       "          0.1486, -0.1063],\n",
-       "        [ 0.1796, -0.0009,  0.1236, -0.0783, -0.0937, -0.0560,  0.0441,  0.0812,\n",
-       "          0.2236, -0.0597]], grad_fn=<AddmmBackward0>)"
+       "tensor([[-0.0824,  0.0285,  0.1192,  0.0922,  0.0465,  0.2007, -0.0262,  0.1639,\n",
+       "         -0.0899,  0.1057],\n",
+       "        [-0.0524,  0.0180,  0.0952,  0.0921, -0.0702,  0.2043,  0.0393,  0.0629,\n",
+       "         -0.1250,  0.0537]], grad_fn=<AddmmBackward0>)"
       ]
      },
      "execution_count": 2,
@@ -55,8 +55,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-03-22T08:08:29.719824050Z",
-     "start_time": "2026-03-22T08:08:29.644546772Z"
+     "end_time": "2026-03-25T12:53:22.230024033Z",
+     "start_time": "2026-03-25T12:53:21.253445153Z"
     }
    },
    "cell_type": "code",
@@ -76,8 +76,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-03-22T08:08:29.957480273Z",
-     "start_time": "2026-03-22T08:08:29.789396471Z"
+     "end_time": "2026-03-25T12:53:22.637036131Z",
+     "start_time": "2026-03-25T12:53:22.314296739Z"
     }
    },
    "cell_type": "code",
@@ -90,10 +90,10 @@
     {
      "data": {
       "text/plain": [
-       "tensor([[ 0.0376, -0.2522, -0.0243, -0.0838,  0.1215,  0.0258, -0.2358,  0.0799,\n",
-       "          0.0756,  0.0520],\n",
-       "        [ 0.0098, -0.2070,  0.0638,  0.1173,  0.0275,  0.0116, -0.0448, -0.0448,\n",
-       "         -0.0309, -0.0976]], grad_fn=<AddmmBackward0>)"
+       "tensor([[-0.1096,  0.0395,  0.1076,  0.0112,  0.1523,  0.0678, -0.4146,  0.1690,\n",
+       "          0.0085, -0.0510],\n",
+       "        [-0.0863,  0.0353,  0.0677, -0.0226,  0.1161,  0.0591, -0.3184,  0.1216,\n",
+       "         -0.0316, -0.1315]], grad_fn=<AddmmBackward0>)"
       ]
      },
      "execution_count": 4,
@@ -106,8 +106,8 @@
   {
    "metadata": {
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-     "end_time": "2026-03-22T08:08:30.177898340Z",
-     "start_time": "2026-03-22T08:08:30.069505281Z"
+     "end_time": "2026-03-25T12:53:23.093212653Z",
+     "start_time": "2026-03-25T12:53:22.726300762Z"
     }
    },
    "cell_type": "code",
@@ -136,8 +136,8 @@
   {
    "metadata": {
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-     "end_time": "2026-03-22T08:08:30.414648562Z",
-     "start_time": "2026-03-22T08:08:30.251182946Z"
+     "end_time": "2026-03-25T12:53:23.496786702Z",
+     "start_time": "2026-03-25T12:53:23.216055780Z"
     }
    },
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@@ -150,7 +150,7 @@
     {
      "data": {
       "text/plain": [
-       "tensor(0.1704, grad_fn=<SumBackward0>)"
+       "tensor(0.2039, grad_fn=<SumBackward0>)"
       ]
      },
      "execution_count": 6,
@@ -163,8 +163,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-03-22T08:08:30.514145240Z",
-     "start_time": "2026-03-22T08:08:30.426612891Z"
+     "end_time": "2026-03-25T12:53:23.718703932Z",
+     "start_time": "2026-03-25T12:53:23.576457566Z"
     }
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    "cell_type": "code",
@@ -187,8 +187,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-03-22T08:08:30.617747011Z",
-     "start_time": "2026-03-22T08:08:30.517586238Z"
+     "end_time": "2026-03-25T12:53:24.088583749Z",
+     "start_time": "2026-03-25T12:53:23.724853929Z"
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    },
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@@ -202,8 +202,8 @@
     {
      "data": {
       "text/plain": [
-       "tensor([[-0.2445],\n",
-       "        [-0.2901]], grad_fn=<AddmmBackward0>)"
+       "tensor([[0.3055],\n",
+       "        [0.0396]], grad_fn=<AddmmBackward0>)"
       ]
      },
      "execution_count": 8,
@@ -216,8 +216,8 @@
   {
    "metadata": {
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-     "end_time": "2026-03-22T08:08:30.825671299Z",
-     "start_time": "2026-03-22T08:08:30.691388202Z"
+     "end_time": "2026-03-25T12:53:24.533854996Z",
+     "start_time": "2026-03-25T12:53:24.227646164Z"
     }
    },
    "cell_type": "code",
@@ -228,7 +228,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "OrderedDict([('weight', tensor([[-0.2116,  0.3448,  0.0726, -0.0626, -0.2922,  0.3172,  0.3025, -0.3025]])), ('bias', tensor([-0.3315]))])\n"
+      "OrderedDict([('weight', tensor([[-0.0619, -0.2581, -0.0887,  0.1497,  0.3016,  0.0745,  0.3351, -0.2275]])), ('bias', tensor([0.1878]))])\n"
      ]
     }
    ],
@@ -237,8 +237,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-03-22T08:08:31.020445691Z",
-     "start_time": "2026-03-22T08:08:30.902305394Z"
+     "end_time": "2026-03-25T12:53:24.907381106Z",
+     "start_time": "2026-03-25T12:53:24.595749565Z"
     }
    },
    "cell_type": "code",
@@ -249,8 +249,8 @@
      "data": {
       "text/plain": [
        "OrderedDict([('weight',\n",
-       "              tensor([[-0.2116,  0.3448,  0.0726, -0.0626, -0.2922,  0.3172,  0.3025, -0.3025]])),\n",
-       "             ('bias', tensor([-0.3315]))])"
+       "              tensor([[-0.0619, -0.2581, -0.0887,  0.1497,  0.3016,  0.0745,  0.3351, -0.2275]])),\n",
+       "             ('bias', tensor([0.1878]))])"
       ]
      },
      "execution_count": 10,
@@ -263,8 +263,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-03-22T08:08:31.127350738Z",
-     "start_time": "2026-03-22T08:08:31.055037575Z"
+     "end_time": "2026-03-25T12:53:25.145444931Z",
+     "start_time": "2026-03-25T12:53:24.912612304Z"
     }
    },
    "cell_type": "code",
@@ -284,8 +284,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-03-22T08:08:31.206008645Z",
-     "start_time": "2026-03-22T08:08:31.139239226Z"
+     "end_time": "2026-03-25T12:53:25.261894811Z",
+     "start_time": "2026-03-25T12:53:25.163843129Z"
     }
    },
    "cell_type": "code",
@@ -300,8 +300,8 @@
      "output_type": "stream",
      "text": [
       "Parameter containing:\n",
-      "tensor([-0.3315], requires_grad=True)\n",
-      "tensor([-0.3315])\n"
+      "tensor([0.1878], requires_grad=True)\n",
+      "tensor([0.1878])\n"
      ]
     }
    ],
@@ -310,8 +310,8 @@
   {
    "metadata": {
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-     "end_time": "2026-03-22T08:08:31.286245677Z",
-     "start_time": "2026-03-22T08:08:31.230728228Z"
+     "end_time": "2026-03-25T12:53:25.341935137Z",
+     "start_time": "2026-03-25T12:53:25.264357977Z"
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@@ -334,8 +334,8 @@
   {
    "metadata": {
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-     "end_time": "2026-03-22T08:08:31.385905750Z",
-     "start_time": "2026-03-22T08:08:31.307506282Z"
+     "end_time": "2026-03-25T12:53:25.433915822Z",
+     "start_time": "2026-03-25T12:53:25.357825225Z"
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@@ -359,8 +359,8 @@
   {
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-     "end_time": "2026-03-22T08:08:31.470489659Z",
-     "start_time": "2026-03-22T08:08:31.391689979Z"
+     "end_time": "2026-03-25T12:53:25.543917851Z",
+     "start_time": "2026-03-25T12:53:25.460879914Z"
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@@ -370,7 +370,7 @@
     {
      "data": {
       "text/plain": [
-       "tensor([-0.3315])"
+       "tensor([0.1878])"
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@@ -383,8 +383,8 @@
   {
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-     "end_time": "2026-03-22T08:08:31.522581812Z",
-     "start_time": "2026-03-22T08:08:31.482437170Z"
+     "end_time": "2026-03-25T12:53:25.617010198Z",
+     "start_time": "2026-03-25T12:53:25.559343957Z"
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@@ -404,8 +404,8 @@
   {
    "metadata": {
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-     "end_time": "2026-03-22T08:08:31.643076590Z",
-     "start_time": "2026-03-22T08:08:31.558403449Z"
+     "end_time": "2026-03-25T12:53:25.713767703Z",
+     "start_time": "2026-03-25T12:53:25.621699911Z"
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@@ -418,8 +418,8 @@
     {
      "data": {
       "text/plain": [
-       "tensor([[-0.3640],\n",
-       "        [-0.3640]], grad_fn=<AddmmBackward0>)"
+       "tensor([[-0.3406],\n",
+       "        [-0.3406]], grad_fn=<AddmmBackward0>)"
       ]
      },
      "execution_count": 17,
@@ -432,8 +432,8 @@
   {
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-     "end_time": "2026-03-22T08:08:31.860114658Z",
-     "start_time": "2026-03-22T08:08:31.722546330Z"
+     "end_time": "2026-03-25T12:53:26.096212878Z",
+     "start_time": "2026-03-25T12:53:25.758161035Z"
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@@ -481,8 +481,8 @@
   {
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-     "end_time": "2026-03-22T08:08:32.103301882Z",
-     "start_time": "2026-03-22T08:08:31.980555778Z"
+     "end_time": "2026-03-25T12:53:26.459785465Z",
+     "start_time": "2026-03-25T12:53:26.247775930Z"
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@@ -492,7 +492,7 @@
     {
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-       "tensor([ 0.3672, -0.3124, -0.3113, -0.3251, -0.4771, -0.3622,  0.1464, -0.4632])"
+       "tensor([ 0.3709, -0.2778, -0.1532, -0.4749,  0.4300, -0.0282, -0.0499,  0.3819])"
       ]
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      "execution_count": 19,
@@ -505,8 +505,8 @@
   {
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-     "end_time": "2026-03-22T08:08:32.231455211Z",
-     "start_time": "2026-03-22T08:08:32.137730392Z"
+     "end_time": "2026-03-25T12:53:26.559898609Z",
+     "start_time": "2026-03-25T12:53:26.465566578Z"
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@@ -523,7 +523,7 @@
     {
      "data": {
       "text/plain": [
-       "(tensor([-0.0004,  0.0166, -0.0085, -0.0099]), tensor(0.))"
+       "(tensor([-0.0090,  0.0195,  0.0008,  0.0062]), tensor(0.))"
       ]
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@@ -536,8 +536,8 @@
   {
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-     "end_time": "2026-03-22T08:08:32.322842445Z",
-     "start_time": "2026-03-22T08:08:32.234982576Z"
+     "end_time": "2026-03-25T12:53:26.624188061Z",
+     "start_time": "2026-03-25T12:53:26.561739279Z"
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@@ -560,7 +560,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "tensor([-0.3265, -0.5057, -0.5062, -0.2116])\n",
+      "tensor([-0.0184,  0.4366, -0.5272,  0.1226])\n",
       "tensor([[42., 42., 42., 42., 42., 42., 42., 42.]])\n"
      ]
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@@ -570,8 +570,8 @@
   {
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-     "end_time": "2026-03-22T08:08:32.377993392Z",
-     "start_time": "2026-03-22T08:08:32.324885649Z"
+     "end_time": "2026-03-25T12:53:26.720471236Z",
+     "start_time": "2026-03-25T12:53:26.641527865Z"
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@@ -586,8 +586,8 @@
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-     "start_time": "2026-03-22T08:08:32.386815096Z"
+     "end_time": "2026-03-25T12:53:26.986419396Z",
+     "start_time": "2026-03-25T12:53:26.727284472Z"
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@@ -613,8 +613,8 @@
   {
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-     "start_time": "2026-03-22T08:08:32.476644136Z"
+     "end_time": "2026-03-25T12:53:27.038073696Z",
+     "start_time": "2026-03-25T12:53:26.998499395Z"
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@@ -638,8 +638,8 @@
   {
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-     "start_time": "2026-03-22T08:08:32.528496997Z"
+     "end_time": "2026-03-25T12:53:27.097281119Z",
+     "start_time": "2026-03-25T12:53:27.040823019Z"
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@@ -651,8 +651,8 @@
   {
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-     "start_time": "2026-03-22T08:08:32.616231856Z"
+     "end_time": "2026-03-25T12:53:27.229604563Z",
+     "start_time": "2026-03-25T12:53:27.100431141Z"
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@@ -682,8 +682,8 @@
   {
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-     "start_time": "2026-03-22T08:08:32.715175504Z"
+     "end_time": "2026-03-25T12:53:27.413849570Z",
+     "start_time": "2026-03-25T12:53:27.245765495Z"
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@@ -710,8 +710,8 @@
   {
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-     "end_time": "2026-03-22T08:08:32.908809253Z",
-     "start_time": "2026-03-22T08:08:32.843784246Z"
+     "end_time": "2026-03-25T12:53:27.819912529Z",
+     "start_time": "2026-03-25T12:53:27.491059110Z"
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@@ -731,8 +731,8 @@
   {
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-     "start_time": "2026-03-22T08:08:33.092115317Z"
+     "end_time": "2026-03-25T12:53:28.107369770Z",
+     "start_time": "2026-03-25T12:53:27.908345229Z"
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@@ -760,8 +760,8 @@
   {
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-     "start_time": "2026-03-22T08:08:33.234892901Z"
+     "end_time": "2026-03-25T12:53:28.483070674Z",
+     "start_time": "2026-03-25T12:53:28.179399310Z"
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@@ -781,8 +781,8 @@
   {
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-     "start_time": "2026-03-22T08:08:33.387838879Z"
+     "end_time": "2026-03-25T12:53:28.940265905Z",
+     "start_time": "2026-03-25T12:53:28.769072795Z"
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@@ -814,8 +814,8 @@
   {
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-     "start_time": "2026-03-22T08:08:33.561038017Z"
+     "end_time": "2026-03-25T12:53:29.204080403Z",
+     "start_time": "2026-03-25T12:53:29.030462580Z"
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@@ -847,8 +847,8 @@
   {
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-     "start_time": "2026-03-22T08:08:33.891686033Z"
+     "end_time": "2026-03-25T12:53:29.646525680Z",
+     "start_time": "2026-03-25T12:53:29.347929714Z"
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@@ -878,8 +878,8 @@
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-     "start_time": "2026-03-22T08:08:34.313636464Z"
+     "end_time": "2026-03-25T12:53:30.137467722Z",
+     "start_time": "2026-03-25T12:53:29.924865950Z"
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@@ -891,8 +891,8 @@
   {
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-     "start_time": "2026-03-22T08:08:34.507329239Z"
+     "end_time": "2026-03-25T12:53:30.333573187Z",
+     "start_time": "2026-03-25T12:53:30.191438502Z"
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@@ -908,8 +908,8 @@
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-     "end_time": "2026-03-22T08:08:35.980584379Z",
-     "start_time": "2026-03-22T08:08:34.640606389Z"
+     "end_time": "2026-03-25T12:53:31.737006650Z",
+     "start_time": "2026-03-25T12:53:30.344801829Z"
     }
    },
    "cell_type": "code",
@@ -930,7 +930,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "epoch 20, loss 0.000\n",
+      "epoch 20, loss 0.003\n",
       "epoch 40, loss 0.000\n",
       "epoch 60, loss 0.000\n",
       "epoch 80, loss 0.000\n",
@@ -943,8 +943,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-03-22T08:08:36.147166039Z",
-     "start_time": "2026-03-22T08:08:36.070619821Z"
+     "end_time": "2026-03-25T12:53:31.954198352Z",
+     "start_time": "2026-03-25T12:53:31.789083268Z"
     }
    },
    "cell_type": "code",
@@ -967,8 +967,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-03-22T08:08:36.349805416Z",
-     "start_time": "2026-03-22T08:08:36.243749022Z"
+     "end_time": "2026-03-25T12:53:32.286815333Z",
+     "start_time": "2026-03-25T12:53:32.015795016Z"
     }
    },
    "cell_type": "code",
@@ -992,8 +992,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-03-22T08:08:36.565573176Z",
-     "start_time": "2026-03-22T08:08:36.473905736Z"
+     "end_time": "2026-03-25T12:53:32.508857009Z",
+     "start_time": "2026-03-25T12:53:32.348271053Z"
     }
    },
    "cell_type": "code",
@@ -1019,8 +1019,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-03-22T08:08:36.629064391Z",
-     "start_time": "2026-03-22T08:08:36.577410135Z"
+     "end_time": "2026-03-25T12:53:32.590919691Z",
+     "start_time": "2026-03-25T12:53:32.513906871Z"
     }
    },
    "cell_type": "code",
@@ -1046,8 +1046,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-03-22T08:08:36.778747354Z",
-     "start_time": "2026-03-22T08:08:36.631642133Z"
+     "end_time": "2026-03-25T12:53:32.717183431Z",
+     "start_time": "2026-03-25T12:53:32.611335875Z"
     }
    },
    "cell_type": "code",
@@ -1073,8 +1073,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-03-22T08:08:36.912486341Z",
-     "start_time": "2026-03-22T08:08:36.816037554Z"
+     "end_time": "2026-03-25T12:53:32.787967768Z",
+     "start_time": "2026-03-25T12:53:32.720890025Z"
     }
    },
    "cell_type": "code",
@@ -1100,8 +1100,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-03-22T08:09:37.230541174Z",
-     "start_time": "2026-03-22T08:09:37.139260256Z"
+     "end_time": "2026-03-25T12:53:32.925224132Z",
+     "start_time": "2026-03-25T12:53:32.820587683Z"
     }
    },
    "cell_type": "code",
@@ -1122,18 +1122,18 @@
        "        [104., 120.]])"
       ]
      },
-     "execution_count": 50,
+     "execution_count": 43,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
-   "execution_count": 50
+   "execution_count": 43
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-03-22T08:09:01.390798830Z",
-     "start_time": "2026-03-22T08:09:01.334900206Z"
+     "end_time": "2026-03-25T12:53:33.185821813Z",
+     "start_time": "2026-03-25T12:53:32.981013074Z"
     }
    },
    "cell_type": "code",
@@ -1143,13 +1143,13 @@
    ],
    "id": "d409110d0d6b4b49",
    "outputs": [],
-   "execution_count": 47
+   "execution_count": 44
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-03-22T08:09:39.731392821Z",
-     "start_time": "2026-03-22T08:09:39.608604541Z"
+     "end_time": "2026-03-25T12:53:33.377776100Z",
+     "start_time": "2026-03-25T12:53:33.230963272Z"
     }
    },
    "cell_type": "code",
@@ -1165,18 +1165,18 @@
        "torch.Size([3, 2, 2, 2])"
       ]
      },
-     "execution_count": 51,
+     "execution_count": 45,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
-   "execution_count": 51
+   "execution_count": 45
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-03-22T08:09:43.297502870Z",
-     "start_time": "2026-03-22T08:09:43.186648920Z"
+     "end_time": "2026-03-25T12:53:33.404945478Z",
+     "start_time": "2026-03-25T12:53:33.381591903Z"
     }
    },
    "cell_type": "code",
@@ -1196,18 +1196,18 @@
        "         [192., 224.]]])"
       ]
      },
-     "execution_count": 52,
+     "execution_count": 46,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
-   "execution_count": 52
+   "execution_count": 46
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-03-22T08:23:20.460754568Z",
-     "start_time": "2026-03-22T08:23:20.424813665Z"
+     "end_time": "2026-03-25T12:53:33.482281628Z",
+     "start_time": "2026-03-25T12:53:33.427984889Z"
     }
    },
    "cell_type": "code",
@@ -1224,13 +1224,13 @@
    ],
    "id": "362d8c692b3c1d75",
    "outputs": [],
-   "execution_count": 56
+   "execution_count": 47
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-03-22T08:23:21.690978973Z",
-     "start_time": "2026-03-22T08:23:21.638506037Z"
+     "end_time": "2026-03-25T12:53:33.539310405Z",
+     "start_time": "2026-03-25T12:53:33.485273899Z"
     }
    },
    "cell_type": "code",
@@ -1240,13 +1240,13 @@
    ],
    "id": "28e761f677df8b16",
    "outputs": [],
-   "execution_count": 57
+   "execution_count": 48
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-03-22T08:23:22.844449890Z",
-     "start_time": "2026-03-22T08:23:22.694694019Z"
+     "end_time": "2026-03-25T12:53:33.644382591Z",
+     "start_time": "2026-03-25T12:53:33.542526101Z"
     }
    },
    "cell_type": "code",
@@ -1262,13 +1262,13 @@
      ]
     }
    ],
-   "execution_count": 58
+   "execution_count": 49
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-03-22T08:24:53.417955565Z",
-     "start_time": "2026-03-22T08:24:53.297421833Z"
+     "end_time": "2026-03-25T12:53:33.715840072Z",
+     "start_time": "2026-03-25T12:53:33.685724533Z"
     }
    },
    "cell_type": "code",
@@ -1278,15 +1278,3368 @@
    ],
    "id": "be28e27d30f36e2c",
    "outputs": [],
+   "execution_count": 50
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:53:33.833762326Z",
+     "start_time": "2026-03-25T12:53:33.752003546Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "def pool2d(X,pool_size,mode='max'):\n",
+    "    p_h,p_w =pool_size\n",
+    "    Y = torch.zeros((X.shape[0]-p_h+1,X.shape[1]-p_w+1))\n",
+    "    for i in range(Y.shape[0]):\n",
+    "        for j in range(Y.shape[1]):\n",
+    "            match mode:\n",
+    "                case 'max':\n",
+    "                    Y[i,j]=X[i:i+p_h,j:j+p_w].max()\n",
+    "                case 'avg':\n",
+    "                    Y[i,j]=X[i:i+p_h,j:j+p_w].mean()\n",
+    "\n",
+    "    return Y"
+   ],
+   "id": "3c3f71349a2e54c0",
+   "outputs": [],
+   "execution_count": 51
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:53:33.941263303Z",
+     "start_time": "2026-03-25T12:53:33.837650145Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "X = torch.tensor([[0.0, 1.0, 2.0], [3.0, 4.0, 5.0], [6.0, 7.0, 8.0]])\n",
+    "pool2d(X, (2, 2))"
+   ],
+   "id": "a67207c861cf0cfd",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "tensor([[4., 5.],\n",
+       "        [7., 8.]])"
+      ]
+     },
+     "execution_count": 52,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "execution_count": 52
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:53:34.291316821Z",
+     "start_time": "2026-03-25T12:53:34.048006688Z"
+    }
+   },
+   "cell_type": "code",
+   "source": "pool2d(X, (2, 2), 'avg')",
+   "id": "e387b48df3831b85",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "tensor([[2., 3.],\n",
+       "        [5., 6.]])"
+      ]
+     },
+     "execution_count": 53,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "execution_count": 53
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:53:34.937892470Z",
+     "start_time": "2026-03-25T12:53:34.524932637Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "X = torch.arange(16, dtype=torch.float32).reshape((1, 1, 4, 4))\n",
+    "X"
+   ],
+   "id": "41b618b3a48522b4",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "tensor([[[[ 0.,  1.,  2.,  3.],\n",
+       "          [ 4.,  5.,  6.,  7.],\n",
+       "          [ 8.,  9., 10., 11.],\n",
+       "          [12., 13., 14., 15.]]]])"
+      ]
+     },
+     "execution_count": 54,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "execution_count": 54
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:53:35.364929618Z",
+     "start_time": "2026-03-25T12:53:35.250760743Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "pool2d=nn.MaxPool2d(3)\n",
+    "pool2d(X)"
+   ],
+   "id": "c77484a8d1267259",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "tensor([[[[10.]]]])"
+      ]
+     },
+     "execution_count": 55,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "execution_count": 55
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:53:35.405212051Z",
+     "start_time": "2026-03-25T12:53:35.381419347Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "pool2d = nn.MaxPool2d(3, padding=1, stride=2)\n",
+    "pool2d(X)"
+   ],
+   "id": "847a2bacfb6f2bd7",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "tensor([[[[ 5.,  7.],\n",
+       "          [13., 15.]]]])"
+      ]
+     },
+     "execution_count": 56,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "execution_count": 56
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:53:35.511354814Z",
+     "start_time": "2026-03-25T12:53:35.428268478Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "pool2d = nn.MaxPool2d((2, 3), stride=(2, 3), padding=(0, 1))\n",
+    "pool2d(X)"
+   ],
+   "id": "5efad1e0b616fff7",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "tensor([[[[ 5.,  7.],\n",
+       "          [13., 15.]]]])"
+      ]
+     },
+     "execution_count": 57,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "execution_count": 57
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:53:35.571965177Z",
+     "start_time": "2026-03-25T12:53:35.523510246Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "X = torch.cat((X, X + 1), 1)\n",
+    "X"
+   ],
+   "id": "386d4b3eb8069328",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "tensor([[[[ 0.,  1.,  2.,  3.],\n",
+       "          [ 4.,  5.,  6.,  7.],\n",
+       "          [ 8.,  9., 10., 11.],\n",
+       "          [12., 13., 14., 15.]],\n",
+       "\n",
+       "         [[ 1.,  2.,  3.,  4.],\n",
+       "          [ 5.,  6.,  7.,  8.],\n",
+       "          [ 9., 10., 11., 12.],\n",
+       "          [13., 14., 15., 16.]]]])"
+      ]
+     },
+     "execution_count": 58,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "execution_count": 58
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:53:35.636903197Z",
+     "start_time": "2026-03-25T12:53:35.575376191Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "pool2d = nn.MaxPool2d(3, padding=1, stride=2)\n",
+    "pool2d(X)"
+   ],
+   "id": "ba5f57a8ca2a3b06",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "tensor([[[[ 5.,  7.],\n",
+       "          [13., 15.]],\n",
+       "\n",
+       "         [[ 6.,  8.],\n",
+       "          [14., 16.]]]])"
+      ]
+     },
+     "execution_count": 59,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "execution_count": 59
   },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:53:35.808804883Z",
+     "start_time": "2026-03-25T12:53:35.667844728Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "net = nn.Sequential(\n",
+    "    nn.Conv2d(1,6,kernel_size=5,padding=2), #1*1*28*28 -> 1*6*28*28\n",
+    "    nn.Sigmoid(),\n",
+    "    nn.AvgPool2d(kernel_size=2, stride=2),  #1*6*28*28 -> 1*6*14*14\n",
+    "    nn.Conv2d(6, 16, kernel_size=5), nn.Sigmoid(), #1*6*14*14 -> 1*16*10*10\n",
+    "    nn.AvgPool2d(kernel_size=2, stride=2), #1*16*10*10 -> 1*16*5*5\n",
+    "    nn.Flatten(),\n",
+    "    nn.Linear(16 * 5 * 5, 120), nn.Sigmoid(),\n",
+    "    nn.Linear(120, 84), nn.Sigmoid(),\n",
+    "    nn.Linear(84, 10)\n",
+    ")\n",
+    "X = torch.rand(size=(1,1,28,28),dtype=torch.float32)\n",
+    "for layer in net:\n",
+    "    X=layer(X)\n",
+    "    print(layer.__class__.__name__,'output shape: \\t',X.shape)"
+   ],
+   "id": "1eabc29f9c838842",
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Conv2d output shape: \t torch.Size([1, 6, 28, 28])\n",
+      "Sigmoid output shape: \t torch.Size([1, 6, 28, 28])\n",
+      "AvgPool2d output shape: \t torch.Size([1, 6, 14, 14])\n",
+      "Conv2d output shape: \t torch.Size([1, 16, 10, 10])\n",
+      "Sigmoid output shape: \t torch.Size([1, 16, 10, 10])\n",
+      "AvgPool2d output shape: \t torch.Size([1, 16, 5, 5])\n",
+      "Flatten output shape: \t torch.Size([1, 400])\n",
+      "Linear output shape: \t torch.Size([1, 120])\n",
+      "Sigmoid output shape: \t torch.Size([1, 120])\n",
+      "Linear output shape: \t torch.Size([1, 84])\n",
+      "Sigmoid output shape: \t torch.Size([1, 84])\n",
+      "Linear output shape: \t torch.Size([1, 10])\n"
+     ]
+    }
+   ],
+   "execution_count": 60
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:36.172500455Z",
+     "start_time": "2026-03-25T12:54:33.846313406Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "import d2l.torch as d2l\n",
+    "batch_size = 256\n",
+    "train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size=batch_size)"
+   ],
+   "id": "e372f75817ad4a0f",
+   "outputs": [],
+   "execution_count": 62
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:36.218171897Z",
+     "start_time": "2026-03-25T12:54:36.201338102Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "lr, num_epochs = 0.9, 10\n",
+    "#d2l.train_ch6(net, train_iter, test_iter, num_epochs, lr, d2l.try_gpu())"
+   ],
+   "id": "9aaeb948f3353955",
+   "outputs": [],
+   "execution_count": 63
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:36.375790030Z",
+     "start_time": "2026-03-25T12:54:36.223406778Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "class Inception(nn.Module):\n",
+    "    def __init__(self,in_channels,c1,c2,c3,c4,**kwargs):\n",
+    "        super(Inception,self).__init__(**kwargs)\n",
+    "        self.p1_1 = nn.Conv2d(in_channels,c1,kernel_size=1)\n",
+    "        self.p2_1 = nn.Conv2d(in_channels,c2[0],kernel_size=1)\n",
+    "        self.p2_2 = nn.Conv2d(c2[0],c2[1],kernel_size=3,padding=1)\n",
+    "        self.p3_1 = nn.Conv2d(in_channels,c3[0],kernel_size=1)\n",
+    "        self.p3_2 = nn.Conv2d(c3[0],c3[1],kernel_size=5,padding=2)\n",
+    "        self.p4_1 = nn.MaxPool2d(kernel_size=3, stride=1, padding=1)\n",
+    "        self.p4_2 = nn.Conv2d(in_channels, c4, kernel_size=1)\n",
+    "    def forward(self,x):\n",
+    "        p1 = F.relu(self.p1_1(x))\n",
+    "        p2 = F.relu(self.p2_2(F.relu(self.p2_1(x))))\n",
+    "        p3 = F.relu(self.p3_2(F.relu(self.p3_1(x))))\n",
+    "        p4 = F.relu(self.p4_2(self.p4_1(x)))\n",
+    "        return torch.cat((p1,p2,p3,p4),dim=1)"
+   ],
+   "id": "6d3bb3f70f297dba",
+   "outputs": [],
+   "execution_count": 64
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:37.582867237Z",
+     "start_time": "2026-03-25T12:54:36.386034018Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "b1 = nn.Sequential(nn.Conv2d(1, 64, kernel_size=7, stride=2, padding=3),\n",
+    "                    nn.ReLU(),\n",
+    "                    nn.MaxPool2d(kernel_size=3, stride=2, padding=1))\n",
+    "b2 = nn.Sequential(nn.Conv2d(64, 64, kernel_size=1),\n",
+    "                    nn.ReLU(),\n",
+    "                    nn.Conv2d(64, 192, kernel_size=3, padding=1),\n",
+    "                    nn.ReLU(),\n",
+    "                    nn.MaxPool2d(kernel_size=3, stride=2, padding=1))\n",
+    "b3 = nn.Sequential(Inception(192, 64, (96, 128), (16, 32), 32),\n",
+    "                    Inception(256, 128, (128, 192), (32, 96), 64),\n",
+    "                    nn.MaxPool2d(kernel_size=3, stride=2, padding=1))\n",
+    "b4 = nn.Sequential(Inception(480, 192, (96, 208), (16, 48), 64),\n",
+    "                    Inception(512, 160, (112, 224), (24, 64), 64),\n",
+    "                    Inception(512, 128, (128, 256), (24, 64), 64),\n",
+    "                    Inception(512, 112, (144, 288), (32, 64), 64),\n",
+    "                    Inception(528, 256, (160, 320), (32, 128), 128),\n",
+    "                    nn.MaxPool2d(kernel_size=3, stride=2, padding=1))\n",
+    "b5 = nn.Sequential(Inception(832, 256, (160, 320), (32, 128), 128),\n",
+    "                    Inception(832, 384, (192, 384), (48, 128), 128),\n",
+    "                    nn.AdaptiveAvgPool2d((1,1)),\n",
+    "                    nn.Flatten())\n",
+    "net = nn.Sequential(b1, b2, b3, b4, b5, nn.Linear(1024, 10))\n",
+    "X = torch.rand(size=(1, 1, 96, 96))\n",
+    "for layer in net:\n",
+    "    X = layer(X)\n",
+    "    print(layer.__class__.__name__,'output shape:\\t', X.shape)"
+   ],
+   "id": "6ef7022bcb288d65",
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Sequential output shape:\t torch.Size([1, 64, 24, 24])\n",
+      "Sequential output shape:\t torch.Size([1, 192, 12, 12])\n",
+      "Sequential output shape:\t torch.Size([1, 480, 6, 6])\n",
+      "Sequential output shape:\t torch.Size([1, 832, 3, 3])\n",
+      "Sequential output shape:\t torch.Size([1, 1024])\n",
+      "Linear output shape:\t torch.Size([1, 10])\n"
+     ]
+    }
+   ],
+   "execution_count": 65
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:39.007400793Z",
+     "start_time": "2026-03-25T12:54:37.697851296Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "import torchinfo\n",
+    "torchinfo.summary(net,(1,1,96,96))"
+   ],
+   "id": "acc019ce7afa4470",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "==========================================================================================\n",
+       "Layer (type:depth-idx)                   Output Shape              Param #\n",
+       "==========================================================================================\n",
+       "Sequential                               [1, 10]                   --\n",
+       "├─Sequential: 1-1                        [1, 64, 24, 24]           --\n",
+       "│    └─Conv2d: 2-1                       [1, 64, 48, 48]           3,200\n",
+       "│    └─ReLU: 2-2                         [1, 64, 48, 48]           --\n",
+       "│    └─MaxPool2d: 2-3                    [1, 64, 24, 24]           --\n",
+       "├─Sequential: 1-2                        [1, 192, 12, 12]          --\n",
+       "│    └─Conv2d: 2-4                       [1, 64, 24, 24]           4,160\n",
+       "│    └─ReLU: 2-5                         [1, 64, 24, 24]           --\n",
+       "│    └─Conv2d: 2-6                       [1, 192, 24, 24]          110,784\n",
+       "│    └─ReLU: 2-7                         [1, 192, 24, 24]          --\n",
+       "│    └─MaxPool2d: 2-8                    [1, 192, 12, 12]          --\n",
+       "├─Sequential: 1-3                        [1, 480, 6, 6]            --\n",
+       "│    └─Inception: 2-9                    [1, 256, 12, 12]          --\n",
+       "│    │    └─Conv2d: 3-1                  [1, 64, 12, 12]           12,352\n",
+       "│    │    └─Conv2d: 3-2                  [1, 96, 12, 12]           18,528\n",
+       "│    │    └─Conv2d: 3-3                  [1, 128, 12, 12]          110,720\n",
+       "│    │    └─Conv2d: 3-4                  [1, 16, 12, 12]           3,088\n",
+       "│    │    └─Conv2d: 3-5                  [1, 32, 12, 12]           12,832\n",
+       "│    │    └─MaxPool2d: 3-6               [1, 192, 12, 12]          --\n",
+       "│    │    └─Conv2d: 3-7                  [1, 32, 12, 12]           6,176\n",
+       "│    └─Inception: 2-10                   [1, 480, 12, 12]          --\n",
+       "│    │    └─Conv2d: 3-8                  [1, 128, 12, 12]          32,896\n",
+       "│    │    └─Conv2d: 3-9                  [1, 128, 12, 12]          32,896\n",
+       "│    │    └─Conv2d: 3-10                 [1, 192, 12, 12]          221,376\n",
+       "│    │    └─Conv2d: 3-11                 [1, 32, 12, 12]           8,224\n",
+       "│    │    └─Conv2d: 3-12                 [1, 96, 12, 12]           76,896\n",
+       "│    │    └─MaxPool2d: 3-13              [1, 256, 12, 12]          --\n",
+       "│    │    └─Conv2d: 3-14                 [1, 64, 12, 12]           16,448\n",
+       "│    └─MaxPool2d: 2-11                   [1, 480, 6, 6]            --\n",
+       "├─Sequential: 1-4                        [1, 832, 3, 3]            --\n",
+       "│    └─Inception: 2-12                   [1, 512, 6, 6]            --\n",
+       "│    │    └─Conv2d: 3-15                 [1, 192, 6, 6]            92,352\n",
+       "│    │    └─Conv2d: 3-16                 [1, 96, 6, 6]             46,176\n",
+       "│    │    └─Conv2d: 3-17                 [1, 208, 6, 6]            179,920\n",
+       "│    │    └─Conv2d: 3-18                 [1, 16, 6, 6]             7,696\n",
+       "│    │    └─Conv2d: 3-19                 [1, 48, 6, 6]             19,248\n",
+       "│    │    └─MaxPool2d: 3-20              [1, 480, 6, 6]            --\n",
+       "│    │    └─Conv2d: 3-21                 [1, 64, 6, 6]             30,784\n",
+       "│    └─Inception: 2-13                   [1, 512, 6, 6]            --\n",
+       "│    │    └─Conv2d: 3-22                 [1, 160, 6, 6]            82,080\n",
+       "│    │    └─Conv2d: 3-23                 [1, 112, 6, 6]            57,456\n",
+       "│    │    └─Conv2d: 3-24                 [1, 224, 6, 6]            226,016\n",
+       "│    │    └─Conv2d: 3-25                 [1, 24, 6, 6]             12,312\n",
+       "│    │    └─Conv2d: 3-26                 [1, 64, 6, 6]             38,464\n",
+       "│    │    └─MaxPool2d: 3-27              [1, 512, 6, 6]            --\n",
+       "│    │    └─Conv2d: 3-28                 [1, 64, 6, 6]             32,832\n",
+       "│    └─Inception: 2-14                   [1, 512, 6, 6]            --\n",
+       "│    │    └─Conv2d: 3-29                 [1, 128, 6, 6]            65,664\n",
+       "│    │    └─Conv2d: 3-30                 [1, 128, 6, 6]            65,664\n",
+       "│    │    └─Conv2d: 3-31                 [1, 256, 6, 6]            295,168\n",
+       "│    │    └─Conv2d: 3-32                 [1, 24, 6, 6]             12,312\n",
+       "│    │    └─Conv2d: 3-33                 [1, 64, 6, 6]             38,464\n",
+       "│    │    └─MaxPool2d: 3-34              [1, 512, 6, 6]            --\n",
+       "│    │    └─Conv2d: 3-35                 [1, 64, 6, 6]             32,832\n",
+       "│    └─Inception: 2-15                   [1, 528, 6, 6]            --\n",
+       "│    │    └─Conv2d: 3-36                 [1, 112, 6, 6]            57,456\n",
+       "│    │    └─Conv2d: 3-37                 [1, 144, 6, 6]            73,872\n",
+       "│    │    └─Conv2d: 3-38                 [1, 288, 6, 6]            373,536\n",
+       "│    │    └─Conv2d: 3-39                 [1, 32, 6, 6]             16,416\n",
+       "│    │    └─Conv2d: 3-40                 [1, 64, 6, 6]             51,264\n",
+       "│    │    └─MaxPool2d: 3-41              [1, 512, 6, 6]            --\n",
+       "│    │    └─Conv2d: 3-42                 [1, 64, 6, 6]             32,832\n",
+       "│    └─Inception: 2-16                   [1, 832, 6, 6]            --\n",
+       "│    │    └─Conv2d: 3-43                 [1, 256, 6, 6]            135,424\n",
+       "│    │    └─Conv2d: 3-44                 [1, 160, 6, 6]            84,640\n",
+       "│    │    └─Conv2d: 3-45                 [1, 320, 6, 6]            461,120\n",
+       "│    │    └─Conv2d: 3-46                 [1, 32, 6, 6]             16,928\n",
+       "│    │    └─Conv2d: 3-47                 [1, 128, 6, 6]            102,528\n",
+       "│    │    └─MaxPool2d: 3-48              [1, 528, 6, 6]            --\n",
+       "│    │    └─Conv2d: 3-49                 [1, 128, 6, 6]            67,712\n",
+       "│    └─MaxPool2d: 2-17                   [1, 832, 3, 3]            --\n",
+       "├─Sequential: 1-5                        [1, 1024]                 --\n",
+       "│    └─Inception: 2-18                   [1, 832, 3, 3]            --\n",
+       "│    │    └─Conv2d: 3-50                 [1, 256, 3, 3]            213,248\n",
+       "│    │    └─Conv2d: 3-51                 [1, 160, 3, 3]            133,280\n",
+       "│    │    └─Conv2d: 3-52                 [1, 320, 3, 3]            461,120\n",
+       "│    │    └─Conv2d: 3-53                 [1, 32, 3, 3]             26,656\n",
+       "│    │    └─Conv2d: 3-54                 [1, 128, 3, 3]            102,528\n",
+       "│    │    └─MaxPool2d: 3-55              [1, 832, 3, 3]            --\n",
+       "│    │    └─Conv2d: 3-56                 [1, 128, 3, 3]            106,624\n",
+       "│    └─Inception: 2-19                   [1, 1024, 3, 3]           --\n",
+       "│    │    └─Conv2d: 3-57                 [1, 384, 3, 3]            319,872\n",
+       "│    │    └─Conv2d: 3-58                 [1, 192, 3, 3]            159,936\n",
+       "│    │    └─Conv2d: 3-59                 [1, 384, 3, 3]            663,936\n",
+       "│    │    └─Conv2d: 3-60                 [1, 48, 3, 3]             39,984\n",
+       "│    │    └─Conv2d: 3-61                 [1, 128, 3, 3]            153,728\n",
+       "│    │    └─MaxPool2d: 3-62              [1, 832, 3, 3]            --\n",
+       "│    │    └─Conv2d: 3-63                 [1, 128, 3, 3]            106,624\n",
+       "│    └─AdaptiveAvgPool2d: 2-20           [1, 1024, 1, 1]           --\n",
+       "│    └─Flatten: 2-21                     [1, 1024]                 --\n",
+       "├─Linear: 1-6                            [1, 10]                   10,250\n",
+       "==========================================================================================\n",
+       "Total params: 5,977,530\n",
+       "Trainable params: 5,977,530\n",
+       "Non-trainable params: 0\n",
+       "Total mult-adds (Units.MEGABYTES): 276.66\n",
+       "==========================================================================================\n",
+       "Input size (MB): 0.04\n",
+       "Forward/backward pass size (MB): 4.74\n",
+       "Params size (MB): 23.91\n",
+       "Estimated Total Size (MB): 28.69\n",
+       "=========================================================================================="
+      ]
+     },
+     "execution_count": 66,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "execution_count": 66
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:40.559617829Z",
+     "start_time": "2026-03-25T12:54:39.231004686Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "lr, num_epochs, batch_size = 0.1, 10, 128\n",
+    "train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size, resize=96)\n",
+    "#d2l.train_ch6(net, train_iter, test_iter, num_epochs, lr, d2l.try_gpu())"
+   ],
+   "id": "3760a5e5813405f7",
+   "outputs": [],
+   "execution_count": 67
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:41.392761415Z",
+     "start_time": "2026-03-25T12:54:40.984224963Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "class Residual(nn.Module):\n",
+    "    def __init__(self,input_channels,num_channels,use_1x1conv=False,strides=1):\n",
+    "        super().__init__()\n",
+    "        self.conv1 = nn.Conv2d(input_channels,num_channels,kernel_size=3,padding=1,stride=strides)\n",
+    "        self.conv2 = nn.Conv2d(num_channels,num_channels,kernel_size=3,padding=1)\n",
+    "        if use_1x1conv:\n",
+    "            self.conv3 = nn.Conv2d(input_channels,num_channels,kernel_size=1,stride=strides)\n",
+    "        else:\n",
+    "            self.conv3= None\n",
+    "        self.bn1=nn.BatchNorm2d(num_channels)\n",
+    "        self.bn2=nn.BatchNorm2d(num_channels)\n",
+    "    def forward(self,X):\n",
+    "        Y=F.relu(self.bn1(self.conv1(X)))\n",
+    "        Y=self.bn2(self.conv2(Y))\n",
+    "        if self.conv3:\n",
+    "            X = self.conv3(X)\n",
+    "        Y+=X\n",
+    "        return F.relu(Y)\n"
+   ],
+   "id": "9300979845ba6916",
+   "outputs": [],
+   "execution_count": 68
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:41.501972047Z",
+     "start_time": "2026-03-25T12:54:41.455568607Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "blk = Residual(3,3)\n",
+    "X = torch.rand(4, 3, 6, 6)"
+   ],
+   "id": "1248323517ff3228",
+   "outputs": [],
+   "execution_count": 69
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:41.680548549Z",
+     "start_time": "2026-03-25T12:54:41.504484009Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "blk = Residual(3,6, use_1x1conv=True, strides=2)\n",
+    "blk(X).shape"
+   ],
+   "id": "82cdbd71a157b51c",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "torch.Size([4, 6, 3, 3])"
+      ]
+     },
+     "execution_count": 70,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "execution_count": 70
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:41.713889764Z",
+     "start_time": "2026-03-25T12:54:41.697804378Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "b1 = nn.Sequential(nn.Conv2d(1, 64, kernel_size=7, stride=2, padding=3),\n",
+    "nn.BatchNorm2d(64), nn.ReLU(),\n",
+    "nn.MaxPool2d(kernel_size=3, stride=2, padding=1))"
+   ],
+   "id": "727da1d2d363ac62",
+   "outputs": [],
+   "execution_count": 71
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:41.769559409Z",
+     "start_time": "2026-03-25T12:54:41.715465374Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "def resnet_block(input_channels, num_channels, num_residuals,\n",
+    "                first_block=False):\n",
+    "    blk = []\n",
+    "    for i in range(num_residuals):\n",
+    "        if i == 0 and not first_block:\n",
+    "            blk.append(Residual(input_channels, num_channels,\n",
+    "                        use_1x1conv=True, strides=2))\n",
+    "        else:\n",
+    "            blk.append(Residual(num_channels, num_channels))\n",
+    "    return blk"
+   ],
+   "id": "124134971f8441c0",
+   "outputs": [],
+   "execution_count": 72
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:41.849526581Z",
+     "start_time": "2026-03-25T12:54:41.773164092Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "b2 = nn.Sequential(*resnet_block(64, 64, 2, first_block=True))\n",
+    "b3 = nn.Sequential(*resnet_block(64, 128, 2))\n",
+    "b4 = nn.Sequential(*resnet_block(128, 256, 2))\n",
+    "b5 = nn.Sequential(*resnet_block(256, 512, 2))"
+   ],
+   "id": "ca1f1c69fba3e913",
+   "outputs": [],
+   "execution_count": 73
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:41.945086842Z",
+     "start_time": "2026-03-25T12:54:41.850992491Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "net = nn.Sequential(b1, b2, b3, b4, b5,\n",
+    "nn.AdaptiveAvgPool2d((1,1)),\n",
+    "nn.Flatten(), nn.Linear(512, 10))"
+   ],
+   "id": "f21db27de5dbdec1",
+   "outputs": [],
+   "execution_count": 74
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:43.021161834Z",
+     "start_time": "2026-03-25T12:54:41.947258256Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "X = torch.rand(size=(1, 1, 224, 224))\n",
+    "for layer in net:\n",
+    "    X = layer(X)\n",
+    "    print(layer.__class__.__name__,'output shape:\\t', X.shape)"
+   ],
+   "id": "6f8851a2bfd18c4e",
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Sequential output shape:\t torch.Size([1, 64, 56, 56])\n",
+      "Sequential output shape:\t torch.Size([1, 64, 56, 56])\n",
+      "Sequential output shape:\t torch.Size([1, 128, 28, 28])\n",
+      "Sequential output shape:\t torch.Size([1, 256, 14, 14])\n",
+      "Sequential output shape:\t torch.Size([1, 512, 7, 7])\n",
+      "AdaptiveAvgPool2d output shape:\t torch.Size([1, 512, 1, 1])\n",
+      "Flatten output shape:\t torch.Size([1, 512])\n",
+      "Linear output shape:\t torch.Size([1, 10])\n"
+     ]
+    }
+   ],
+   "execution_count": 75
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:43.115617383Z",
+     "start_time": "2026-03-25T12:54:43.046016884Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "lr, num_epochs, batch_size = 0.05, 10, 256\n",
+    "train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size, resize=96)\n",
+    "#d2l.train_ch6(net, train_iter, test_iter, num_epochs, lr, d2l.try_gpu())"
+   ],
+   "id": "e095d74b29dffef6",
+   "outputs": [],
+   "execution_count": 76
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:43.222301703Z",
+     "start_time": "2026-03-25T12:54:43.119038826Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "import torch\n",
+    "import d2l.torch as d2l\n",
+    "import numpy\n",
+    "import torch.nn as nn\n",
+    "import torch.nn.functional as F\n",
+    "print(torch.version.__version__)"
+   ],
+   "id": "3fd6d22221f87bea",
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "2.10.0+cu128\n"
+     ]
+    }
+   ],
+   "execution_count": 77
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:43.326030676Z",
+     "start_time": "2026-03-25T12:54:43.296999050Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "A=torch.Tensor([[1,2,0,0],[0,2,0,0],[0,0,2,1],[0,0,0,3]])\n",
+    "C=torch.Tensor([[1,0,0,0],[0,1,0,0],[0,0,-2,3],[0,0,0,-3]])"
+   ],
+   "id": "254f5d3d659dbe0f",
+   "outputs": [],
+   "execution_count": 78
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:43.395079338Z",
+     "start_time": "2026-03-25T12:54:43.332112143Z"
+    }
+   },
+   "cell_type": "code",
+   "source": "B=torch.Tensor([[2,0,0,0],[-2,1,0,0],[0,0,-3,0],[0,0,0,-3]])",
+   "id": "a13d9c27c2fdbfad",
+   "outputs": [],
+   "execution_count": 79
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:43.526691390Z",
+     "start_time": "2026-03-25T12:54:43.405681993Z"
+    }
+   },
+   "cell_type": "code",
+   "source": "torch.mm(A,C)",
+   "id": "e513a37beaa85f8f",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "tensor([[ 1.,  2.,  0.,  0.],\n",
+       "        [ 0.,  2.,  0.,  0.],\n",
+       "        [ 0.,  0., -4.,  3.],\n",
+       "        [ 0.,  0.,  0., -9.]])"
+      ]
+     },
+     "execution_count": 80,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "execution_count": 80
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:44.183397512Z",
+     "start_time": "2026-03-25T12:54:43.839736167Z"
+    }
+   },
+   "cell_type": "code",
+   "source": "torch.det(torch.mm(torch.mm(A,C),B))",
+   "id": "9a85eceac652875f",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "tensor(1296.)"
+      ]
+     },
+     "execution_count": 81,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "execution_count": 81
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:44.470157150Z",
+     "start_time": "2026-03-25T12:54:44.297718949Z"
+    }
+   },
+   "cell_type": "code",
+   "source": "1296**5\n",
+   "id": "6dc27d79722da58f",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "3656158440062976"
+      ]
+     },
+     "execution_count": 82,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "execution_count": 82
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:44.641680344Z",
+     "start_time": "2026-03-25T12:54:44.488342487Z"
+    }
+   },
+   "cell_type": "code",
+   "source": "torch.mm(C,B)",
+   "id": "ec5a170d775f4705",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "tensor([[ 2.,  0.,  0.,  0.],\n",
+       "        [-2.,  1.,  0.,  0.],\n",
+       "        [ 0.,  0.,  6., -9.],\n",
+       "        [ 0.,  0.,  0.,  9.]])"
+      ]
+     },
+     "execution_count": 83,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "execution_count": 83
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:45.007541962Z",
+     "start_time": "2026-03-25T12:54:44.731090643Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "T = 1000 # 总共产生1000个点\n",
+    "time = torch.arange(1, T + 1, dtype=torch.float32)\n",
+    "x = torch.sin(0.01 * time) + torch.normal(0, 0.2, (T,))\n",
+    "d2l.plot(time, [x], 'time', 'x', xlim=[1, 1000], figsize=(6, 3))"
+   ],
+   "id": "c3884b10464c6baa",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<Figure size 600x300 with 1 Axes>"
+      ],
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+     },
+     "metadata": {},
+     "output_type": "display_data",
+     "jetTransient": {
+      "display_id": null
+     }
+    }
+   ],
+   "execution_count": 84
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:45.287386804Z",
+     "start_time": "2026-03-25T12:54:45.068746693Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "tau = 4\n",
+    "features = torch.zeros((T - tau, tau))\n",
+    "for i in range(tau):\n",
+    "    features[:, i] = x[i: T - tau + i]\n",
+    "labels = x[tau:].reshape((-1, 1))\n",
+    "x,features,labels\n"
+   ],
+   "id": "5d450c6f6b724a14",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(tensor([-0.1257,  0.4977,  0.1275,  0.0113,  0.1759,  0.1263,  0.0984,  0.0670,\n",
+       "          0.3374, -0.3129,  0.3756,  0.0234, -0.0841,  0.4951,  0.3441, -0.0585,\n",
+       "         -0.2159,  0.0357,  0.0667, -0.0126,  0.6966, -0.0548,  0.0864,  0.5669,\n",
+       "          0.2040,  0.2158,  0.1378,  0.2790,  0.4541,  0.3656,  0.3050,  0.3321,\n",
+       "          0.3818,  0.3404,  0.3803,  0.3527,  0.5237,  0.7250,  0.3400,  0.3136,\n",
+       "          0.6944,  0.3985,  0.9682,  0.5841,  0.5376,  0.2229,  0.6266,  0.1417,\n",
+       "          0.2132,  0.6786,  0.3201,  0.5340,  0.7747,  0.7968,  0.7266,  0.7018,\n",
+       "          0.8106,  0.6221,  0.2093,  0.3683,  0.5998,  0.5546,  0.6686,  0.4981,\n",
+       "          0.6079,  0.3726,  0.9469,  0.6261,  0.4213,  0.5943,  1.2487,  0.5027,\n",
+       "          0.6524,  0.6218,  0.4721,  0.7688,  0.8629,  0.5897,  0.3414,  1.0822,\n",
+       "          0.9223,  0.8020,  0.6607,  0.4673,  0.7155,  0.6349,  0.4676,  0.9303,\n",
+       "          0.6977,  0.7986,  0.5661,  0.9401,  0.8111,  1.0929,  0.5887,  0.8674,\n",
+       "          0.8081,  0.8682,  0.7049,  1.0303,  0.5297,  0.8990,  0.6131,  1.1693,\n",
+       "          1.0146,  1.1179,  0.8550,  0.6801,  0.9054,  0.9622,  0.8227,  0.6969,\n",
+       "          0.8629,  0.9992,  0.9735,  0.9114,  0.5090,  0.9698,  1.1530,  1.2176,\n",
+       "          1.1019,  1.0681,  0.6768,  1.0307,  0.9873,  1.1988,  1.1947,  0.8704,\n",
+       "          0.8378,  0.7581,  1.2643,  1.2095,  0.7556,  1.0024,  0.8649,  1.1953,\n",
+       "          0.8106,  1.2512,  1.1907,  0.8453,  1.0807,  0.7710,  0.9226,  0.8100,\n",
+       "          1.0641,  0.9683,  0.7675,  1.2630,  0.9153,  1.0170,  1.3423,  0.8989,\n",
+       "          1.2243,  1.3355,  0.9849,  0.6055,  0.4062,  0.8255,  1.1904,  0.7565,\n",
+       "          1.0362,  0.8106,  0.8765,  1.1825,  1.0300,  1.1883,  0.7432,  0.7962,\n",
+       "          0.7900,  0.9459,  1.0081,  1.1498,  1.0555,  1.4386,  0.9888,  0.7890,\n",
+       "          0.9454,  0.9568,  0.9832,  0.7835,  0.8084,  0.7282,  1.1450,  1.2708,\n",
+       "          1.1315,  0.6742,  0.6001,  0.6483,  0.8992,  1.0016,  1.0392,  0.5630,\n",
+       "          1.3330,  0.9323,  0.6719,  0.9954,  1.0855,  1.0105,  0.6578,  1.0974,\n",
+       "          0.9163,  1.0161,  1.0866,  0.8661,  0.5516,  1.0398,  1.0476,  0.8525,\n",
+       "          0.8723,  1.0883,  0.5629,  0.3963,  0.7161,  1.2104,  1.0025,  1.0816,\n",
+       "          0.7881,  0.7980,  0.6719,  0.5641,  0.7839,  0.7183,  0.6777,  1.1626,\n",
+       "          0.6991,  0.7296,  0.9149,  0.4818,  0.3593,  0.8057,  0.9782,  0.6981,\n",
+       "          0.8359,  0.5616,  0.8751,  0.4524,  0.9480,  0.4057,  0.6413,  0.6728,\n",
+       "          0.8040,  1.1152,  0.6752,  0.7030,  0.5862,  0.7373,  0.6680,  0.6739,\n",
+       "          0.7372,  1.0807,  0.8491,  0.4628,  0.5695,  0.4675,  0.8295,  0.7881,\n",
+       "          0.6622,  0.3701,  0.3987,  0.6082,  0.4924,  0.6136,  0.4755,  0.7166,\n",
+       "          0.4721,  0.2420,  0.2503,  0.5961,  0.5344,  0.6053,  0.5369,  0.2291,\n",
+       "          0.3503,  0.2833,  0.1630,  0.0821,  0.1769,  0.5129,  0.2650,  0.1519,\n",
+       "          0.2660,  0.1505,  0.2407,  0.1766,  0.2215,  0.3759,  0.0643,  0.2909,\n",
+       "          0.0220,  0.5878,  0.1559,  0.2339,  0.3533, -0.1447,  0.5657,  0.0656,\n",
+       "         -0.1913,  0.1975, -0.0296,  0.3531,  0.0032,  0.1607,  0.2249,  0.0783,\n",
+       "          0.1663, -0.0781, -0.0607,  0.3047,  0.2461, -0.0380,  0.0481, -0.0040,\n",
+       "          0.0110, -0.0221,  0.1001,  0.0754,  0.2153, -0.1584,  0.0033, -0.2072,\n",
+       "          0.1622, -0.1114, -0.0954, -0.2582, -0.0575, -0.0883,  0.3422, -0.1808,\n",
+       "         -0.2768, -0.1964,  0.1526, -0.1362,  0.0674, -0.5093, -0.0344, -0.3681,\n",
+       "         -0.2217, -0.1733, -0.0589, -0.1194, -0.0979, -0.2122, -0.5427, -0.5028,\n",
+       "          0.0059, -0.2044, -0.2778, -0.3447, -0.0537, -0.4030, -0.7130, -0.5167,\n",
+       "         -0.4477, -0.4382,  0.0076, -0.1804, -0.1491,  0.1210, -0.4279, -0.6204,\n",
+       "         -0.7309, -0.1835, -0.9354, -0.6655, -0.7265, -0.5585, -0.8215, -0.3998,\n",
+       "         -0.6667, -0.4026, -0.3606, -0.2286, -0.5571, -0.8246, -0.2567, -0.8022,\n",
+       "         -0.3873, -0.6781, -0.8021, -0.7463, -0.6887, -0.5723, -0.6661, -0.4324,\n",
+       "         -0.6482, -0.5130, -0.6848, -0.5460, -0.8493, -0.1809, -0.5165, -0.4671,\n",
+       "         -0.8529, -0.9896, -0.8904, -0.4498, -1.0809, -0.9123, -0.7125, -0.4627,\n",
+       "         -0.5643, -0.7416, -0.8990, -0.8161, -0.5500, -0.9439, -0.8327, -0.7132,\n",
+       "         -0.8250, -0.9772, -0.8947, -0.4970, -0.4945, -0.4604, -0.7029, -0.7518,\n",
+       "         -0.7635, -0.8060, -0.8300, -1.1194, -1.2429, -0.7834, -0.3628, -1.1099,\n",
+       "         -0.8337, -1.0767, -0.7193, -0.6253, -0.9703, -0.5913, -1.0695, -0.9610,\n",
+       "         -0.7796, -0.8729, -1.1516, -0.8974, -1.1277, -0.8297, -0.6336, -1.5144,\n",
+       "         -1.0980, -1.0812, -0.5136, -0.6882, -0.9138, -0.9021, -1.0671, -1.1456,\n",
+       "         -0.9467, -0.6042, -0.8922, -0.9499, -0.6512, -1.0729, -1.1589, -1.1675,\n",
+       "         -0.9637, -0.7511, -0.8479, -0.8410, -1.1934, -0.8869, -0.9340, -1.0252,\n",
+       "         -0.8195, -1.3040, -0.6508, -1.0083, -1.1282, -0.9536, -1.0764, -1.2750,\n",
+       "         -1.0073, -1.0259, -0.8144, -1.2082, -0.9558, -0.9895, -1.0417, -1.0077,\n",
+       "         -0.7460, -0.7199, -1.1118, -0.7411, -1.2156, -0.8967, -0.8194, -1.1041,\n",
+       "         -0.9286, -0.9155, -0.7483, -0.9874, -1.0476, -0.9132, -0.7950, -0.8823,\n",
+       "         -0.8565, -1.0017, -0.9736, -0.8743, -0.9509, -1.3399, -0.8861, -1.0557,\n",
+       "         -0.8494, -0.6369, -1.0813, -0.7510, -0.8624, -1.1163, -0.9114, -0.7323,\n",
+       "         -0.9083, -0.8352, -0.6851, -0.9174, -0.9412, -1.3040, -0.6257, -0.7814,\n",
+       "         -0.7670, -1.0620, -0.9168, -1.0231, -0.5532, -0.7955, -0.9293, -0.7984,\n",
+       "         -0.9475, -0.8074, -1.0046, -0.7866, -0.8110, -0.8169, -0.7929, -0.9577,\n",
+       "         -0.7490, -0.6953, -0.7600, -0.6348, -0.5752, -0.6600, -1.1377, -1.0344,\n",
+       "         -0.6518, -0.7506, -0.9227, -0.7814, -0.9301, -0.4463, -0.8153, -0.7221,\n",
+       "         -0.6543, -1.0062, -0.4462, -0.5389, -0.3644, -0.3854, -0.5175, -0.3598,\n",
+       "         -0.7745, -0.8278, -0.6843, -0.5519, -0.6849, -0.6662, -0.8282, -0.5927,\n",
+       "         -0.8346, -0.5149, -0.0033, -0.7285, -0.8659, -0.4320, -0.5433, -0.5551,\n",
+       "         -0.4936, -0.3990, -0.2697, -0.5388, -0.5527, -0.5663, -0.4017, -0.2667,\n",
+       "         -0.3446, -0.3117, -0.3110, -0.8562, -0.2726, -0.5014, -0.4719, -0.5338,\n",
+       "         -0.7666, -0.1854, -0.5822, -0.4734, -0.2585, -0.2755, -0.4047, -0.0902,\n",
+       "         -0.0984, -0.3434, -0.0755, -0.5209, -0.2434, -0.3536, -0.0617,  0.1276,\n",
+       "         -0.0150, -0.5196, -0.2691, -0.8314,  0.1469, -0.0438, -0.4816,  0.1779,\n",
+       "         -0.1709, -0.2126, -0.2875, -0.4329, -0.0967, -0.5540, -0.2296, -0.0021,\n",
+       "         -0.1871,  0.0261, -0.0573,  0.3196,  0.1587,  0.1620, -0.3062,  0.1800,\n",
+       "         -0.0216, -0.0861,  0.3876,  0.2574,  0.2573,  0.3694,  0.1312,  0.6010,\n",
+       "          0.0274,  0.0227, -0.1395,  0.0214,  0.3586,  0.0331,  0.2754,  0.4699,\n",
+       "          0.3533, -0.0946,  0.1566,  0.2768,  0.6166,  0.3522,  0.2357,  0.2673,\n",
+       "          0.2506,  0.4461,  0.6163,  0.1398,  0.3288,  0.4211,  0.3313,  0.1029,\n",
+       "          0.4284,  0.1385,  0.1132,  0.0989,  0.3567,  0.2329,  0.4514,  0.7074,\n",
+       "          0.3183,  0.2934,  0.4533,  0.2790,  0.4807,  0.8162,  0.6992,  0.1948,\n",
+       "          0.5107,  0.8306,  0.2990,  0.2718,  0.7156,  0.8072,  0.6706,  0.5840,\n",
+       "          0.8009,  0.5367,  0.8542,  0.4551,  0.6621,  0.6004,  0.6589,  0.4726,\n",
+       "          0.5991,  0.8084,  0.5788,  0.7125,  0.6552,  0.9191,  0.3361,  0.8335,\n",
+       "          0.2599,  0.6830,  0.6857,  0.4505,  0.7303,  0.5562,  0.3135,  0.7432,\n",
+       "          0.8188,  0.7189,  0.6228,  0.8273,  0.6486,  0.9803,  0.6484,  0.7697,\n",
+       "          1.1531,  0.9866,  1.3931,  0.9747,  1.2460,  1.0597,  0.7014,  0.9013,\n",
+       "          0.9571,  0.7041,  1.0944,  1.1762,  1.1356,  1.0760,  1.0171,  0.8546,\n",
+       "          0.9204,  0.9524,  1.3716,  0.7630,  0.9069,  1.0180,  1.0366,  1.0358,\n",
+       "          0.8609,  0.8634,  0.8047,  0.7477,  0.9808,  1.0275,  1.2071,  0.5799,\n",
+       "          0.8834,  0.8784,  1.1447,  1.0891,  0.5811,  0.9703,  1.2833,  0.9937,\n",
+       "          1.1356,  0.8306,  0.9129,  1.0194,  1.4320,  1.2589,  0.9175,  0.8849,\n",
+       "          1.1727,  0.9605,  0.7599,  0.8099,  1.0688,  0.7013,  1.0260,  0.7066,\n",
+       "          0.8967,  1.0578,  0.8639,  1.0968,  0.9553,  1.0410,  0.7809,  0.8928,\n",
+       "          0.9644,  0.8980,  0.9744,  0.6657,  1.0549,  0.9716,  1.0272,  0.9510,\n",
+       "          1.0992,  0.8345,  1.0305,  1.0269,  0.9503,  1.0622,  0.9953,  1.3019,\n",
+       "          1.0447,  0.9759,  0.9953,  1.0697,  0.9619,  1.0681,  1.0844,  0.6814,\n",
+       "          0.7774,  1.1827,  1.1599,  0.7436,  0.8570,  0.7392,  1.2210,  0.8350,\n",
+       "          0.7613,  0.7885,  1.0991,  0.6867,  0.5461,  1.1209,  1.1265,  0.9876,\n",
+       "          0.8403,  0.9892,  0.7838,  0.5770,  0.7996,  1.1023,  1.1888,  0.8290,\n",
+       "          0.9919,  0.7272,  0.6149,  0.8744,  0.7331,  0.9389,  0.8888,  0.4813,\n",
+       "          1.1600,  0.6871,  0.7780,  0.9699,  0.3082,  0.8391,  0.5978,  0.5697,\n",
+       "          0.9227,  0.4502,  0.5293,  0.7309,  0.7579,  0.5995,  0.5698,  0.5490,\n",
+       "          0.7483,  0.9721,  0.9419,  0.5393,  0.9869,  0.9892,  0.5714,  0.7620,\n",
+       "          0.6800,  0.8412,  0.6070,  0.1774,  0.6198,  0.7153,  0.7985,  0.5209,\n",
+       "          1.1309,  0.6716,  0.7221,  0.5309,  0.6143,  0.9212,  0.6585,  0.5518,\n",
+       "          0.7676,  0.7002,  0.5711,  0.5491,  0.7280,  1.2188,  0.3206,  0.5493,\n",
+       "          0.7454,  0.5868,  0.6143,  0.8513,  0.1876,  0.5672,  0.4292,  0.5437,\n",
+       "          0.4909,  0.7139,  0.5861,  0.3725,  0.5194,  0.4843,  0.0279,  0.3152,\n",
+       "          0.4333,  0.5915,  0.2709,  0.4861,  0.1708, -0.0844,  0.1523, -0.2092,\n",
+       "          0.2965, -0.1280,  0.4479,  0.4392,  0.1969,  0.1989, -0.0969,  0.2829,\n",
+       "          0.1741, -0.1890, -0.0512,  0.4777,  0.0458,  0.0724,  0.1996,  0.2772,\n",
+       "         -0.0650,  0.4351,  0.2693, -0.0298, -0.1171,  0.3714,  0.0992,  0.0090,\n",
+       "          0.0618,  0.1225,  0.1389,  0.1166,  0.0821,  0.0435, -0.1259, -0.1045,\n",
+       "          0.1779, -0.2051, -0.2457, -0.1619, -0.0991,  0.1651,  0.1712, -0.1440,\n",
+       "         -0.0499, -0.0943,  0.1058, -0.3224, -0.2115, -0.1307, -0.2432, -0.1935,\n",
+       "         -0.1462, -0.3798, -0.3857, -0.3871,  0.1132, -0.5729,  0.1458, -0.5250,\n",
+       "         -0.1113, -0.1085, -0.3974, -0.2798, -0.2995, -0.0517, -0.1601, -0.5213,\n",
+       "         -0.3897, -0.5143, -0.4268, -0.4268, -0.1593, -0.3720, -0.2030, -0.5328,\n",
+       "         -0.8009, -0.5220, -0.5291, -0.3730, -0.4571, -0.3859, -0.3053, -0.3744,\n",
+       "         -0.7439, -0.7338, -0.2856, -0.3440, -0.6041, -0.7940, -0.6112, -0.1943]),\n",
+       " tensor([[-0.1257,  0.4977,  0.1275,  0.0113],\n",
+       "         [ 0.4977,  0.1275,  0.0113,  0.1759],\n",
+       "         [ 0.1275,  0.0113,  0.1759,  0.1263],\n",
+       "         ...,\n",
+       "         [-0.7338, -0.2856, -0.3440, -0.6041],\n",
+       "         [-0.2856, -0.3440, -0.6041, -0.7940],\n",
+       "         [-0.3440, -0.6041, -0.7940, -0.6112]]),\n",
+       " tensor([[ 0.1759],\n",
+       "         [ 0.1263],\n",
+       "         [ 0.0984],\n",
+       "         [ 0.0670],\n",
+       "         [ 0.3374],\n",
+       "         [-0.3129],\n",
+       "         [ 0.3756],\n",
+       "         [ 0.0234],\n",
+       "         [-0.0841],\n",
+       "         [ 0.4951],\n",
+       "         [ 0.3441],\n",
+       "         [-0.0585],\n",
+       "         [-0.2159],\n",
+       "         [ 0.0357],\n",
+       "         [ 0.0667],\n",
+       "         [-0.0126],\n",
+       "         [ 0.6966],\n",
+       "         [-0.0548],\n",
+       "         [ 0.0864],\n",
+       "         [ 0.5669],\n",
+       "         [ 0.2040],\n",
+       "         [ 0.2158],\n",
+       "         [ 0.1378],\n",
+       "         [ 0.2790],\n",
+       "         [ 0.4541],\n",
+       "         [ 0.3656],\n",
+       "         [ 0.3050],\n",
+       "         [ 0.3321],\n",
+       "         [ 0.3818],\n",
+       "         [ 0.3404],\n",
+       "         [ 0.3803],\n",
+       "         [ 0.3527],\n",
+       "         [ 0.5237],\n",
+       "         [ 0.7250],\n",
+       "         [ 0.3400],\n",
+       "         [ 0.3136],\n",
+       "         [ 0.6944],\n",
+       "         [ 0.3985],\n",
+       "         [ 0.9682],\n",
+       "         [ 0.5841],\n",
+       "         [ 0.5376],\n",
+       "         [ 0.2229],\n",
+       "         [ 0.6266],\n",
+       "         [ 0.1417],\n",
+       "         [ 0.2132],\n",
+       "         [ 0.6786],\n",
+       "         [ 0.3201],\n",
+       "         [ 0.5340],\n",
+       "         [ 0.7747],\n",
+       "         [ 0.7968],\n",
+       "         [ 0.7266],\n",
+       "         [ 0.7018],\n",
+       "         [ 0.8106],\n",
+       "         [ 0.6221],\n",
+       "         [ 0.2093],\n",
+       "         [ 0.3683],\n",
+       "         [ 0.5998],\n",
+       "         [ 0.5546],\n",
+       "         [ 0.6686],\n",
+       "         [ 0.4981],\n",
+       "         [ 0.6079],\n",
+       "         [ 0.3726],\n",
+       "         [ 0.9469],\n",
+       "         [ 0.6261],\n",
+       "         [ 0.4213],\n",
+       "         [ 0.5943],\n",
+       "         [ 1.2487],\n",
+       "         [ 0.5027],\n",
+       "         [ 0.6524],\n",
+       "         [ 0.6218],\n",
+       "         [ 0.4721],\n",
+       "         [ 0.7688],\n",
+       "         [ 0.8629],\n",
+       "         [ 0.5897],\n",
+       "         [ 0.3414],\n",
+       "         [ 1.0822],\n",
+       "         [ 0.9223],\n",
+       "         [ 0.8020],\n",
+       "         [ 0.6607],\n",
+       "         [ 0.4673],\n",
+       "         [ 0.7155],\n",
+       "         [ 0.6349],\n",
+       "         [ 0.4676],\n",
+       "         [ 0.9303],\n",
+       "         [ 0.6977],\n",
+       "         [ 0.7986],\n",
+       "         [ 0.5661],\n",
+       "         [ 0.9401],\n",
+       "         [ 0.8111],\n",
+       "         [ 1.0929],\n",
+       "         [ 0.5887],\n",
+       "         [ 0.8674],\n",
+       "         [ 0.8081],\n",
+       "         [ 0.8682],\n",
+       "         [ 0.7049],\n",
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+       "         [-0.1943]]))"
+      ]
+     },
+     "execution_count": 85,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "execution_count": 85
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:45.359640179Z",
+     "start_time": "2026-03-25T12:54:45.318414005Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "batch_size, n_train = 16, 600\n",
+    "# 只有前n_train个样本用于训练\n",
+    "train_iter = d2l.load_array((features[:n_train], labels[:n_train]),\n",
+    "batch_size, is_train=True)\n"
+   ],
+   "id": "239a596b20d40dec",
+   "outputs": [],
+   "execution_count": 86
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:45.428803377Z",
+     "start_time": "2026-03-25T12:54:45.361568655Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "def init_weights(m):\n",
+    "    if type(m) == nn.Linear:\n",
+    "        nn.init.xavier_uniform_(m.weight)"
+   ],
+   "id": "54d30bd0ee41cb8",
+   "outputs": [],
+   "execution_count": 87
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:45.522687266Z",
+     "start_time": "2026-03-25T12:54:45.432893670Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "def get_net():\n",
+    "    net = nn.Sequential(nn.Linear(4, 10),\n",
+    "    nn.ReLU(),\n",
+    "    nn.Linear(10, 1))\n",
+    "    net.apply(init_weights)\n",
+    "    return net\n",
+    "loss = nn.MSELoss(reduction='none')"
+   ],
+   "id": "5d095792e3b3681",
+   "outputs": [],
+   "execution_count": 88
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:45.821846960Z",
+     "start_time": "2026-03-25T12:54:45.527750802Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "def train(net, train_iter, loss, epochs, lr):\n",
+    "    trainer = torch.optim.Adam(net.parameters(), lr)\n",
+    "    for epoch in range(epochs):\n",
+    "        for X, y in train_iter:\n",
+    "            trainer.zero_grad()\n",
+    "            l = loss(net(X), y)\n",
+    "            l.sum().backward()\n",
+    "            trainer.step()\n",
+    "        print(f'epoch {epoch + 1}, '\n",
+    "                f'loss: {d2l.evaluate_loss(net, train_iter, loss):f}')\n",
+    "net = get_net()\n",
+    "train(net, train_iter, loss, 5, 0.01)"
+   ],
+   "id": "5c1dba484e805335",
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "epoch 1, loss: 0.069361\n",
+      "epoch 2, loss: 0.057280\n",
+      "epoch 3, loss: 0.054714\n",
+      "epoch 4, loss: 0.054167\n",
+      "epoch 5, loss: 0.050941\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/home/yukun/.conda/envs/nn/lib/python3.11/site-packages/d2l/torch.py:3179: UserWarning: Converting a tensor with requires_grad=True to a scalar may lead to unexpected behavior.\n",
+      "Consider using tensor.detach() first. (Triggered internally at /pytorch/torch/csrc/autograd/generated/python_variable_methods.cpp:836.)\n",
+      "  self.data = [a + float(b) for a, b in zip(self.data, args)]\n"
+     ]
+    }
+   ],
+   "execution_count": 89
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:46.022554993Z",
+     "start_time": "2026-03-25T12:54:45.826680707Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "onestep_preds = net(features)\n",
+    "d2l.plot([time, time[tau:]],\n",
+    "[x.detach().numpy(), onestep_preds.detach().numpy()], 'time',\n",
+    "'x', legend=['data', '1-step preds'], xlim=[1, 1000],\n",
+    "figsize=(6, 3))"
+   ],
+   "id": "a6efb4a978cd9375",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<Figure size 600x300 with 1 Axes>"
+      ],
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131.900475 \nL 193.252829 138.720643 \nL 193.587965 137.252533 \nL 193.9231 127.872076 \nL 194.258235 124.985718 \nL 195.26364 133.232416 \nL 195.598775 126.522168 \nL 195.93391 128.320127 \nL 196.269046 124.392623 \nL 196.604181 126.807042 \nL 196.939316 132.921498 \nL 197.274451 130.338441 \nL 197.609586 130.962164 \nL 197.944721 133.985533 \nL 198.279856 134.538685 \nL 198.614992 134.464342 \nL 198.950127 136.577129 \nL 199.285262 129.395659 \nL 199.620397 132.634744 \nL 199.955532 140.985355 \nL 200.290667 137.554787 \nL 200.625802 137.875176 \nL 200.960938 124.808312 \nL 201.296073 126.504049 \nL 201.631208 126.833453 \nL 202.301478 137.695348 \nL 202.636613 138.030391 \nL 203.306883 127.99069 \nL 203.642019 129.958196 \nL 203.977154 126.662246 \nL 204.312289 129.090438 \nL 204.647424 136.210477 \nL 204.982559 138.769442 \nL 205.317694 139.428592 \nL 205.987965 130.65301 \nL 206.3231 129.359687 \nL 206.99337 135.287023 \nL 207.328505 132.842384 \nL 207.66364 135.43365 \nL 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+     },
+     "metadata": {},
+     "output_type": "display_data",
+     "jetTransient": {
+      "display_id": null
+     }
+    }
+   ],
+   "execution_count": 90
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:46.309387018Z",
+     "start_time": "2026-03-25T12:54:46.060491885Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "multistep_preds = torch.zeros(T)\n",
+    "multistep_preds[: n_train + tau] = x[: n_train + tau]\n",
+    "for i in range(n_train + tau, T):\n",
+    "    multistep_preds[i] = net(\n",
+    "        multistep_preds[i - tau:i].reshape((1, -1)))\n",
+    "d2l.plot([time, time[tau:], time[n_train + tau:]],\n",
+    "            [x.detach().numpy(), onestep_preds.detach().numpy(),\n",
+    "            multistep_preds[n_train + tau:].detach().numpy()], 'time',\n",
+    "            'x', legend=['data', '1-step preds', 'multistep preds'],\n",
+    "                xlim=[1, 1000], figsize=(6, 3))"
+   ],
+   "id": "12c3a1c3912da4dd",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<Figure size 600x300 with 1 Axes>"
+      ],
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124.550127 48.066463 \nL 124.885262 47.560194 \nL 125.555532 59.5333 \nL 125.890667 48.280811 \nL 126.225802 51.637558 \nL 126.560938 53.716881 \nL 126.896073 28.890021 \nL 127.231208 52.621631 \nL 127.566343 51.06401 \nL 127.901478 41.574216 \nL 128.236613 63.74882 \nL 128.571748 70.019436 \nL 128.906883 47.165663 \nL 129.242019 38.330426 \nL 129.577154 52.673714 \nL 129.912289 45.618189 \nL 130.247424 59.662031 \nL 130.582559 43.613997 \nL 130.917694 65.253368 \nL 131.252829 39.877021 \nL 131.587965 67.647106 \nL 131.9231 55.584426 \nL 132.258235 53.968969 \nL 132.59337 47.251393 \nL 132.928505 31.315582 \nL 133.26364 53.847941 \nL 133.598775 52.421004 \nL 133.93391 58.404217 \nL 134.269046 50.66857 \nL 134.604181 54.215942 \nL 134.939316 53.911484 \nL 135.274451 50.672589 \nL 135.609586 33.086206 \nL 135.944721 44.942636 \nL 136.279856 64.7198 \nL 136.614992 59.257069 \nL 136.950127 64.48199 \nL 137.285262 45.94596 \nL 137.620397 48.065935 \nL 137.955532 54.514006 \nL 138.290667 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+     },
+     "metadata": {},
+     "output_type": "display_data",
+     "jetTransient": {
+      "display_id": null
+     }
+    }
+   ],
+   "execution_count": 91
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:46.389774559Z",
+     "start_time": "2026-03-25T12:54:46.333788807Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "import collections\n",
+    "import re"
+   ],
+   "id": "aab66c10a4c143d2",
+   "outputs": [],
+   "execution_count": 92
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:46.511151557Z",
+     "start_time": "2026-03-25T12:54:46.396367087Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "d2l.DATA_HUB['time_machine'] = (d2l.DATA_URL + 'timemachine.txt',\n",
+    "'090b5e7e70c295757f55df93cb0a180b9691891a')\n",
+    "def read_time_machine(): #@save\n",
+    "    \"\"\"将时间机器数据集加载到文本行的列表中\"\"\"\n",
+    "    with open(d2l.download('time_machine'), 'r') as f:\n",
+    "        lines = f.readlines()\n",
+    "    return [re.sub('[^A-Za-z]+', ' ', line).strip().lower() for line in lines]\n",
+    "lines = read_time_machine()\n",
+    "print(f'# 文本总行数: {len(lines)}')\n",
+    "print(lines[0])\n",
+    "print(lines[10])"
+   ],
+   "id": "1aff117af810525e",
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "# 文本总行数: 3221\n",
+      "the time machine by h g wells\n",
+      "twinkled and his usually pale face was flushed and animated the\n"
+     ]
+    }
+   ],
+   "execution_count": 93
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:46.589883911Z",
+     "start_time": "2026-03-25T12:54:46.524677647Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "def tokenize(lines, token='word'): #@save\n",
+    "    \"\"\"将文本行拆分为单词或字符词元\"\"\"\n",
+    "    if token == 'word':\n",
+    "        return [line.split() for line in lines]\n",
+    "    elif token == 'char':\n",
+    "        return [list(line) for line in lines]\n",
+    "    else:\n",
+    "        print('错误：未知词元类型：' + token)\n",
+    "tokens = tokenize(lines)\n",
+    "for i in range(11):\n",
+    "    print(tokens[i])"
+   ],
+   "id": "eb4fe9745fbaa5e2",
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "['the', 'time', 'machine', 'by', 'h', 'g', 'wells']\n",
+      "[]\n",
+      "[]\n",
+      "[]\n",
+      "[]\n",
+      "['i']\n",
+      "[]\n",
+      "[]\n",
+      "['the', 'time', 'traveller', 'for', 'so', 'it', 'will', 'be', 'convenient', 'to', 'speak', 'of', 'him']\n",
+      "['was', 'expounding', 'a', 'recondite', 'matter', 'to', 'us', 'his', 'grey', 'eyes', 'shone', 'and']\n",
+      "['twinkled', 'and', 'his', 'usually', 'pale', 'face', 'was', 'flushed', 'and', 'animated', 'the']\n"
+     ]
+    }
+   ],
+   "execution_count": 94
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:46.684454112Z",
+     "start_time": "2026-03-25T12:54:46.620352826Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "def count_corpus(tokens): #@save\n",
+    "    \"\"\"统计词元的频率\"\"\"\n",
+    "    # 这里的tokens是1D列表或2D列表\n",
+    "    if len(tokens) == 0 or isinstance(tokens[0], list):\n",
+    "    # 将词元列表展平成一个列表\n",
+    "        tokens = [token for line in tokens for token in line]\n",
+    "    return collections.Counter(tokens)\n",
+    "class Vocab: #@save\n",
+    "    \"\"\"文本词表\"\"\"\n",
+    "    def __init__(self, tokens=None, min_freq=0, reserved_tokens=None):\n",
+    "        if tokens is None:\n",
+    "            tokens = []\n",
+    "        if reserved_tokens is None:\n",
+    "            reserved_tokens = []\n",
+    "        # 按出现频率排序\n",
+    "        counter = count_corpus(tokens)\n",
+    "        self._token_freqs = sorted(counter.items(), key=lambda x: x[1],\n",
+    "                                    reverse=True)\n",
+    "        # 未知词元的索引为0\n",
+    "        self.idx_to_token = ['<unk>'] + reserved_tokens\n",
+    "        self.token_to_idx = {token: idx\n",
+    "                                for idx, token in enumerate(self.idx_to_token)}\n",
+    "        for token, freq in self._token_freqs:\n",
+    "            if freq < min_freq:\n",
+    "                break\n",
+    "            if token not in self.token_to_idx:\n",
+    "                self.idx_to_token.append(token)\n",
+    "                self.token_to_idx[token] = len(self.idx_to_token) - 1\n",
+    "    def __len__(self):\n",
+    "        return len(self.idx_to_token)\n",
+    "    def __getitem__(self, tokens):\n",
+    "        if not isinstance(tokens, (list, tuple)):\n",
+    "            return self.token_to_idx.get(tokens, self.unk)\n",
+    "        return [self.__getitem__(token) for token in tokens]\n",
+    "    def to_tokens(self, indices):\n",
+    "        if not isinstance(indices, (list, tuple)):\n",
+    "            return self.idx_to_token[indices]\n",
+    "        return [self.idx_to_token[index] for index in indices]\n",
+    "    @property\n",
+    "    def unk(self): # 未知词元的索引为0\n",
+    "        return 0\n",
+    "    @property\n",
+    "    def token_freqs(self):\n",
+    "        return self._token_freqs"
+   ],
+   "id": "bee8e5d7b798c6c",
+   "outputs": [],
+   "execution_count": 95
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:46.844584420Z",
+     "start_time": "2026-03-25T12:54:46.709821817Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "vocab = Vocab(tokens)\n",
+    "print(list(vocab.token_to_idx.items())[:10])"
+   ],
+   "id": "ff4e8ac2044850b7",
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[('<unk>', 0), ('the', 1), ('i', 2), ('and', 3), ('of', 4), ('a', 5), ('to', 6), ('was', 7), ('in', 8), ('that', 9)]\n"
+     ]
+    }
+   ],
+   "execution_count": 96
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:46.914064266Z",
+     "start_time": "2026-03-25T12:54:46.846539992Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "for i in [0, 100]:\n",
+    "    print('文本:', tokens[i])\n",
+    "    print('索引:', vocab[tokens[i]])"
+   ],
+   "id": "a4e569dfbd251608",
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "文本: ['the', 'time', 'machine', 'by', 'h', 'g', 'wells']\n",
+      "索引: [1, 19, 50, 40, 2183, 2184, 400]\n",
+      "文本: ['were', 'three', 'dimensional', 'representations', 'of', 'his', 'four', 'dimensioned']\n",
+      "索引: [20, 175, 1452, 2250, 4, 25, 262, 2251]\n"
+     ]
+    }
+   ],
+   "execution_count": 97
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:47.087077440Z",
+     "start_time": "2026-03-25T12:54:46.945943096Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "def load_corpus_time_machine(max_tokens=-1): #@save\n",
+    "    \"\"\"返回时光机器数据集的词元索引列表和词表\"\"\"\n",
+    "    lines = read_time_machine()\n",
+    "    tokens = tokenize(lines, 'char')\n",
+    "    vocab = Vocab(tokens)\n",
+    "    # 因为时光机器数据集中的每个文本行不一定是一个句子或一个段落，\n",
+    "    # 所以将所有文本行展平到一个列表中\n",
+    "    corpus = [vocab[token] for line in tokens for token in line]\n",
+    "    if max_tokens > 0:\n",
+    "        corpus = corpus[:max_tokens]\n",
+    "    return corpus, vocab\n",
+    "corpus, vocab = load_corpus_time_machine()\n",
+    "\n",
+    "len(corpus), len(vocab)\n"
+   ],
+   "id": "1b5c1776ae47af5c",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(170580, 28)"
+      ]
+     },
+     "execution_count": 98,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "execution_count": 98
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:47.245364838Z",
+     "start_time": "2026-03-25T12:54:47.111205224Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "tokens = d2l.tokenize(read_time_machine())\n",
+    "# 因为每个文本行不一定是一个句子或一个段落，因此我们把所有文本行拼接到一起\n",
+    "corpus = [token for line in tokens for token in line]\n",
+    "vocab = d2l.Vocab(corpus)\n",
+    "vocab.token_freqs[:10]"
+   ],
+   "id": "99deb85c025e5cdd",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[('the', 2261),\n",
+       " ('i', 1267),\n",
+       " ('and', 1245),\n",
+       " ('of', 1155),\n",
+       " ('a', 816),\n",
+       " ('to', 695),\n",
+       " ('was', 552),\n",
+       " ('in', 541),\n",
+       " ('that', 443),\n",
+       " ('my', 440)]"
+      ]
+     },
+     "execution_count": 99,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "execution_count": 99
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:47.857887916Z",
+     "start_time": "2026-03-25T12:54:47.247469243Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "freqs = [freq for token, freq in vocab.token_freqs]\n",
+    "d2l.plot(freqs, xlabel='token: x', ylabel='frequency: n(x)',\n",
+    "xscale='log', yscale='log')"
+   ],
+   "id": "5c0d846673e16c33",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
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+      ],
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+     },
+     "metadata": {},
+     "output_type": "display_data",
+     "jetTransient": {
+      "display_id": null
+     }
+    }
+   ],
+   "execution_count": 100
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:48.002182407Z",
+     "start_time": "2026-03-25T12:54:47.912592290Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "bigram_tokens = [pair for pair in zip(corpus[:-1], corpus[1:])]\n",
+    "bigram_vocab = Vocab(bigram_tokens)\n",
+    "bigram_vocab.token_freqs[:10]"
+   ],
+   "id": "2826e3ab0863ee64",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[(('of', 'the'), 309),\n",
+       " (('in', 'the'), 169),\n",
+       " (('i', 'had'), 130),\n",
+       " (('i', 'was'), 112),\n",
+       " (('and', 'the'), 109),\n",
+       " (('the', 'time'), 102),\n",
+       " (('it', 'was'), 99),\n",
+       " (('to', 'the'), 85),\n",
+       " (('as', 'i'), 78),\n",
+       " (('of', 'a'), 73)]"
+      ]
+     },
+     "execution_count": 101,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "execution_count": 101
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:48.095243055Z",
+     "start_time": "2026-03-25T12:54:48.005003927Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "trigram_tokens = [triple for triple in zip(\n",
+    "corpus[:-2], corpus[1:-1], corpus[2:])]\n",
+    "trigram_vocab = Vocab(trigram_tokens)\n",
+    "trigram_vocab.token_freqs[:10]"
+   ],
+   "id": "7c8cd0544bf872bb",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[(('the', 'time', 'traveller'), 59),\n",
+       " (('the', 'time', 'machine'), 30),\n",
+       " (('the', 'medical', 'man'), 24),\n",
+       " (('it', 'seemed', 'to'), 16),\n",
+       " (('it', 'was', 'a'), 15),\n",
+       " (('here', 'and', 'there'), 15),\n",
+       " (('seemed', 'to', 'me'), 14),\n",
+       " (('i', 'did', 'not'), 14),\n",
+       " (('i', 'saw', 'the'), 13),\n",
+       " (('i', 'began', 'to'), 13)]"
+      ]
+     },
+     "execution_count": 102,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "execution_count": 102
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:48.748052730Z",
+     "start_time": "2026-03-25T12:54:48.097673111Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "bigram_freqs = [freq for token, freq in bigram_vocab.token_freqs]\n",
+    "trigram_freqs = [freq for token, freq in trigram_vocab.token_freqs]\n",
+    "d2l.plot([freqs, bigram_freqs, trigram_freqs], xlabel='token: x',\n",
+    "ylabel='frequency: n(x)', xscale='log', yscale='log',\n",
+    "legend=['unigram', 'bigram', 'trigram'])"
+   ],
+   "id": "dc3d97dda738613d",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<Figure size 350x250 with 1 Axes>"
+      ],
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+     },
+     "metadata": {},
+     "output_type": "display_data",
+     "jetTransient": {
+      "display_id": null
+     }
+    }
+   ],
+   "execution_count": 103
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:48.898844389Z",
+     "start_time": "2026-03-25T12:54:48.827838521Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "import random\n",
+    "def seq_data_iter_random(corpus, batch_size, num_steps): #@save\n",
+    "    \"\"\"使用随机抽样生成一个小批量子序列\"\"\"\n",
+    "    # 从随机偏移量开始对序列进行分区，随机范围包括num_steps-1\n",
+    "    corpus = corpus[random.randint(0, num_steps - 1):]\n",
+    "    # 减去1，是因为我们需要考虑标签\n",
+    "    num_subseqs = (len(corpus) - 1) // num_steps\n",
+    "    # 长度为num_steps的子序列的起始索引\n",
+    "    initial_indices = list(range(0, num_subseqs * num_steps, num_steps))\n",
+    "    # 在随机抽样的迭代过程中，\n",
+    "    # 来自两个相邻的、随机的、小批量中的子序列不一定在原始序列上相邻\n",
+    "    random.shuffle(initial_indices)\n",
+    "    def data(pos):\n",
+    "    # 返回从pos位置开始的长度为num_steps的序列\n",
+    "        return corpus[pos: pos + num_steps]\n",
+    "    num_batches = num_subseqs // batch_size\n",
+    "    for i in range(0, batch_size * num_batches, batch_size):\n",
+    "        # 在这里，initial_indices包含子序列的随机起始索引\n",
+    "        initial_indices_per_batch = initial_indices[i: i + batch_size]\n",
+    "        X = [data(j) for j in initial_indices_per_batch]\n",
+    "        Y = [data(j + 1) for j in initial_indices_per_batch]\n",
+    "        yield torch.tensor(X), torch.tensor(Y)"
+   ],
+   "id": "fd015793938b83ab",
+   "outputs": [],
+   "execution_count": 104
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:49.053830957Z",
+     "start_time": "2026-03-25T12:54:48.902512374Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "my_seq = list(range(35))\n",
+    "for X, Y in seq_data_iter_random(my_seq, batch_size=2, num_steps=5):\n",
+    "    print('X: ', X, '\\nY:', Y)"
+   ],
+   "id": "8961f4934b8c7cc",
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "X:  tensor([[27, 28, 29, 30, 31],\n",
+      "        [ 2,  3,  4,  5,  6]]) \n",
+      "Y: tensor([[28, 29, 30, 31, 32],\n",
+      "        [ 3,  4,  5,  6,  7]])\n",
+      "X:  tensor([[17, 18, 19, 20, 21],\n",
+      "        [22, 23, 24, 25, 26]]) \n",
+      "Y: tensor([[18, 19, 20, 21, 22],\n",
+      "        [23, 24, 25, 26, 27]])\n",
+      "X:  tensor([[12, 13, 14, 15, 16],\n",
+      "        [ 7,  8,  9, 10, 11]]) \n",
+      "Y: tensor([[13, 14, 15, 16, 17],\n",
+      "        [ 8,  9, 10, 11, 12]])\n"
+     ]
+    }
+   ],
+   "execution_count": 105
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T12:54:49.085900056Z",
+     "start_time": "2026-03-25T12:54:49.065678273Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "def seq_data_iter_sequential(corpus, batch_size, num_steps): #@save\n",
+    "    \"\"\"使用顺序分区生成一个小批量子序列\"\"\"\n",
+    "    # 从随机偏移量开始划分序列\n",
+    "    offset = random.randint(0, num_steps)\n",
+    "    num_tokens = ((len(corpus) - offset - 1) // batch_size) * batch_size\n",
+    "    Xs = torch.tensor(corpus[offset: offset + num_tokens])\n",
+    "    Ys = torch.tensor(corpus[offset + 1: offset + 1 + num_tokens])\n",
+    "    Xs, Ys = Xs.reshape(batch_size, -1), Ys.reshape(batch_size, -1)\n",
+    "    num_batches = Xs.shape[1] // num_steps\n",
+    "    for i in range(0, num_steps * num_batches, num_steps):\n",
+    "        X = Xs[:, i: i + num_steps]\n",
+    "        Y = Ys[:, i: i + num_steps]\n",
+    "        yield X, Y"
+   ],
+   "id": "621b66c0614b22da",
+   "outputs": [],
+   "execution_count": 106
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T13:13:22.060317841Z",
+     "start_time": "2026-03-25T13:13:22.007573330Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "class SeqDataLoader:\n",
+    "    \"\"\"加载序列数据的迭代器\"\"\"\n",
+    "    def __init__(self, batch_size, num_steps, use_random_iter, max_tokens):\n",
+    "        if use_random_iter:\n",
+    "            self.data_iter_fn = seq_data_iter_random\n",
+    "        else:\n",
+    "            self.data_iter_fn = seq_data_iter_sequential\n",
+    "        self.corpus, self.vocab = load_corpus_time_machine(max_tokens)\n",
+    "        self.batch_size, self.num_steps = batch_size, num_steps\n",
+    "    def __iter__(self):\n",
+    "        return self.data_iter_fn(self.corpus, self.batch_size, self.num_steps)\n",
+    "def load_data_time_machine(batch_size, num_steps, #@save\n",
+    "                            use_random_iter=False, max_tokens=10000):\n",
+    "    \"\"\"返回时光机器数据集的迭代器和词表\"\"\"\n",
+    "    data_iter = SeqDataLoader(\n",
+    "    batch_size, num_steps, use_random_iter, max_tokens)\n",
+    "    return data_iter, data_iter.vocab"
+   ],
+   "id": "f09fe2507a925fe9",
+   "outputs": [],
+   "execution_count": 111
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T13:13:25.998507190Z",
+     "start_time": "2026-03-25T13:13:25.902583940Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "batch_size, num_steps = 32, 35\n",
+    "train_iter, vocab = load_data_time_machine(batch_size, num_steps)"
+   ],
+   "id": "69272a664d3b9ae1",
+   "outputs": [],
+   "execution_count": 112
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T13:14:32.469873183Z",
+     "start_time": "2026-03-25T13:14:32.366446697Z"
+    }
+   },
+   "cell_type": "code",
+   "source": "F.one_hot(torch.tensor([0,2]),len(vocab))",
+   "id": "35806d36e5ec3ca7",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "tensor([[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
+       "         0, 0, 0, 0],\n",
+       "        [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
+       "         0, 0, 0, 0]])"
+      ]
+     },
+     "execution_count": 115,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "execution_count": 115
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T13:16:48.087534183Z",
+     "start_time": "2026-03-25T13:16:47.919685613Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "X = torch.arange(10).reshape((2, 5))\n",
+    "F.one_hot(X.T, 28).shape"
+   ],
+   "id": "6a4695284b898013",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "torch.Size([5, 2, 28])"
+      ]
+     },
+     "execution_count": 119,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "execution_count": 119
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T13:37:28.354220059Z",
+     "start_time": "2026-03-25T13:37:28.262974202Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "def get_params(vocab_size, num_hiddens, device):\n",
+    "    num_inputs = num_outputs = vocab_size\n",
+    "    def normal(shape):\n",
+    "        return torch.randn(size=shape, device=device) * 0.01\n",
+    "    # 隐藏层参数\n",
+    "    W_xh = normal((num_inputs, num_hiddens))\n",
+    "    W_hh = normal((num_hiddens, num_hiddens))\n",
+    "    b_h = torch.zeros(num_hiddens, device=device)\n",
+    "    # 输出层参数\n",
+    "    W_hq = normal((num_hiddens, num_outputs))\n",
+    "    b_q = torch.zeros(num_outputs, device=device)\n",
+    "    # 附加梯度\n",
+    "    params = [W_xh, W_hh, b_h, W_hq, b_q]\n",
+    "    '''\n",
+    "    W_xh x->H_t\n",
+    "    W_hh H_t-1->H_t\n",
+    "    W_hq H_t->opt\n",
+    "    '''\n",
+    "    for param in params:\n",
+    "        param.requires_grad_(True)\n",
+    "    return params\n",
+    "def init_rnn_state(batch_size, num_hiddens, device):\n",
+    "    return (torch.zeros((batch_size, num_hiddens), device=device), )\n",
+    "def rnn(inputs,state,params):\n",
+    "    W_xh,W_hh,b_h,W_hq,b_q = params\n",
+    "    H, = state\n",
+    "    outputs = []\n",
+    "    for X in inputs: # X (batchs,vocab)\n",
+    "        H = torch.tanh(torch.mm(X,W_xh)+torch.mm(H,W_hh)+b_h)\n",
+    "        Y = torch.mm(H,W_hq)+b_q\n",
+    "        outputs.append(Y)\n",
+    "    return torch.cat(outputs,dim=0),(H,)\n",
+    "class RNNModelScratch: #@save\n",
+    "    \"\"\"从零开始实现的循环神经网络模型\"\"\"\n",
+    "    def __init__(self, vocab_size, num_hiddens, device,\n",
+    "                get_params, init_state, forward_fn):\n",
+    "        self.vocab_size, self.num_hiddens = vocab_size, num_hiddens\n",
+    "        self.params = get_params(vocab_size, num_hiddens, device)\n",
+    "        self.init_state, self.forward_fn = init_state, forward_fn\n",
+    "    def __call__(self, X, state):\n",
+    "        X = F.one_hot(X.T, self.vocab_size).type(torch.float32)\n",
+    "        return self.forward_fn(X, state, self.params)\n",
+    "    def begin_state(self, batch_size, device):\n",
+    "        return self.init_state(batch_size, self.num_hiddens, device)"
+   ],
+   "id": "405f7c6af8bdd939",
+   "outputs": [],
+   "execution_count": 120
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T13:50:48.023098387Z",
+     "start_time": "2026-03-25T13:50:47.712386114Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "num_hiddens = 512\n",
+    "net = RNNModelScratch(len(vocab), num_hiddens, d2l.try_gpu(), get_params,\n",
+    "init_rnn_state, rnn)\n",
+    "state = net.begin_state(X.shape[0], d2l.try_gpu())\n",
+    "Y, new_state = net(X.to(d2l.try_gpu()), state)\n",
+    "Y.shape, len(new_state), new_state[0].shape"
+   ],
+   "id": "7bdd0b37b1458ec2",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(torch.Size([10, 28]), 1, torch.Size([2, 512]))"
+      ]
+     },
+     "execution_count": 123,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "execution_count": 123
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T14:06:25.042155295Z",
+     "start_time": "2026-03-25T14:06:24.593900625Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "def predict_ch8(prefix, num_preds, net, vocab, device): #@save\n",
+    "    \"\"\"在prefix后面生成新字符\"\"\"\n",
+    "    state = net.begin_state(batch_size=1, device=device)\n",
+    "    outputs = [vocab[prefix[0]]]\n",
+    "    get_input = lambda: torch.tensor([outputs[-1]], device=device).reshape((1, 1))\n",
+    "    for y in prefix[1:]: # 预热期\n",
+    "        _, state = net(get_input(), state)\n",
+    "        outputs.append(vocab[y])\n",
+    "    for _ in range(num_preds): # 预测num_preds步\n",
+    "        y, state = net(get_input(), state)\n",
+    "        outputs.append(int(y.argmax(dim=1).reshape(1)))\n",
+    "    return ''.join([vocab.idx_to_token[i] for i in outputs])\n",
+    "predict_ch8('time traveller ', 10, net, vocab, d2l.try_gpu())"
+   ],
+   "id": "f38dbe2b11e02bc2",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'time traveller slgm sl sl'"
+      ]
+     },
+     "execution_count": 124,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "execution_count": 124
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T14:14:43.788897281Z",
+     "start_time": "2026-03-25T14:14:43.657537187Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "def grad_clipping(net, theta): #@save\n",
+    "    \"\"\"裁剪梯度\"\"\"\n",
+    "    if isinstance(net, nn.Module):\n",
+    "        params = [p for p in net.parameters() if p.requires_grad]\n",
+    "    else:\n",
+    "        params = net.params\n",
+    "    norm = torch.sqrt(sum(torch.sum((p.grad ** 2)) for p in params))\n",
+    "    if norm > theta:\n",
+    "        for param in params:\n",
+    "            param.grad[:] *= theta / norm"
+   ],
+   "id": "6c19717736ffbc68",
+   "outputs": [],
+   "execution_count": 125
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T14:21:41.754553299Z",
+     "start_time": "2026-03-25T14:21:41.701446937Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "import math\n",
+    "def train_epoch_ch8(net, train_iter, loss, updater, device, use_random_iter):\n",
+    "    \"\"\"训练网络一个迭代周期（定义见第8章）\"\"\"\n",
+    "    state, timer = None, d2l.Timer()\n",
+    "    metric = d2l.Accumulator(2) # 训练损失之和,词元数量\n",
+    "    for X, Y in train_iter:\n",
+    "        if state is None or use_random_iter:\n",
+    "            # 在第一次迭代或使用随机抽样时初始化state\n",
+    "            state = net.begin_state(batch_size=X.shape[0], device=device)\n",
+    "        else:\n",
+    "            if isinstance(net, nn.Module) and not isinstance(state, tuple):\n",
+    "                # state对于nn.GRU是个张量\n",
+    "                state.detach_()\n",
+    "            else:\n",
+    "                # state对于nn.LSTM或对于我们从零开始实现的模型是个张量\n",
+    "                for s in state:\n",
+    "                    s.detach_()\n",
+    "        y = Y.T.reshape(-1)\n",
+    "        X, y = X.to(device), y.to(device)\n",
+    "        y_hat, state = net(X, state)\n",
+    "        l = loss(y_hat, y.long()).mean()\n",
+    "        if isinstance(updater, torch.optim.Optimizer):\n",
+    "            updater.zero_grad()\n",
+    "            l.backward()\n",
+    "            grad_clipping(net, 1)\n",
+    "            updater.step()\n",
+    "        else:\n",
+    "            l.backward()\n",
+    "            grad_clipping(net, 1)\n",
+    "            # 因为已经调用了mean函数\n",
+    "            updater(batch_size=1)\n",
+    "        metric.add(l * y.numel(), y.numel())\n",
+    "    return math.exp(metric[0]/metric[1]),metric[1]/timer.stop()\n"
+   ],
+   "id": "37ef611dedcb714b",
+   "outputs": [],
+   "execution_count": 132
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T15:00:52.669519274Z",
+     "start_time": "2026-03-25T15:00:52.618407065Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "def train_ch8(net, train_iter, vocab, lr, num_epochs, device,\n",
+    "use_random_iter=False):\n",
+    "    \"\"\"训练模型（定义见第8章）\"\"\"\n",
+    "    loss = nn.CrossEntropyLoss()\n",
+    "    animator = d2l.Animator(xlabel='epoch', ylabel='perplexity',\n",
+    "                            legend=['train'], xlim=[10, num_epochs])\n",
+    "    # 初始化\n",
+    "    if isinstance(net, nn.Module):\n",
+    "        updater = torch.optim.SGD(net.parameters(), lr)\n",
+    "    else:\n",
+    "        updater = lambda batch_size: d2l.sgd(net.params, lr, batch_size)\n",
+    "    predict = lambda prefix: predict_ch8(prefix, 50, net, vocab, device)\n",
+    "    # 训练和预测\n",
+    "    for epoch in range(num_epochs):\n",
+    "        ppl, speed = train_epoch_ch8(\n",
+    "                            net, train_iter, loss, updater, device, use_random_iter)\n",
+    "        if (epoch + 1) % 10 == 0:\n",
+    "            print(predict('time traveller'))\n",
+    "            animator.add(epoch + 1, [ppl])\n",
+    "    print(f'困惑度 {ppl:.1f}, {speed:.1f} 词元/秒 {str(device)}')\n",
+    "    print(predict('time traveller'))\n",
+    "    print(predict('traveller'))"
+   ],
+   "id": "c96b60b55664378a",
+   "outputs": [],
+   "execution_count": 146
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T15:02:40.728313868Z",
+     "start_time": "2026-03-25T15:00:53.106582989Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "num_epochs, lr = 500, 1\n",
+    "train_ch8(net, train_iter, vocab, lr, num_epochs, d2l.try_gpu())"
+   ],
+   "id": "ab4a2fbf4dfd21ef",
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "困惑度 1.3, 128113.6 词元/秒 cpu\n",
+      "time travelleris thene by in psmed the k waile to se pas of sour\n",
+      "traveller tore asmethe which we canle wey thard abthof spar\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "<Figure size 350x250 with 1 Axes>"
+      ],
+      "image/svg+xml": "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"246.284375pt\" height=\"183.35625pt\" viewBox=\"0 0 246.284375 183.35625\" xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\">\n <metadata>\n  <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n   <cc:Work>\n    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n    <dc:date>2026-03-25T23:02:40.690662</dc:date>\n    <dc:format>image/svg+xml</dc:format>\n    <dc:creator>\n     <cc:Agent>\n      <dc:title>Matplotlib v3.7.2, https://matplotlib.org/</dc:title>\n     </cc:Agent>\n    </dc:creator>\n   </cc:Work>\n  </rdf:RDF>\n </metadata>\n <defs>\n  <style type=\"text/css\">*{stroke-linejoin: round; stroke-linecap: 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+     },
+     "metadata": {},
+     "output_type": "display_data",
+     "jetTransient": {
+      "display_id": null
+     }
+    }
+   ],
+   "execution_count": 147
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T15:02:40.837383063Z",
+     "start_time": "2026-03-25T15:02:40.788068670Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "batch_size, num_steps = 32, 35\n",
+    "train_iter, vocab = load_data_time_machine(batch_size, num_steps)"
+   ],
+   "id": "74d672745751714",
+   "outputs": [],
+   "execution_count": 148
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T15:02:40.907873399Z",
+     "start_time": "2026-03-25T15:02:40.840147997Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "num_hiddens = 256\n",
+    "rnn_layer = nn.RNN(len(vocab), num_hiddens)\n",
+    "state = torch.zeros((1,batch_size,num_hiddens))\n",
+    "X = torch.rand(size=(num_steps, batch_size, len(vocab)))\n",
+    "Y, state_new = rnn_layer(X, state)\n",
+    "Y.shape, state_new.shape"
+   ],
+   "id": "9694c029c9e657e8",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(torch.Size([35, 32, 256]), torch.Size([1, 32, 256]))"
+      ]
+     },
+     "execution_count": 149,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "execution_count": 149
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T15:02:40.960240439Z",
+     "start_time": "2026-03-25T15:02:40.909528103Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "class RNNModel(nn.Module):\n",
+    "    \"\"\"循环神经网络模型\"\"\"\n",
+    "    def __init__(self, rnn_layer, vocab_size, **kwargs):\n",
+    "        super(RNNModel, self).__init__(**kwargs)\n",
+    "        self.rnn = rnn_layer\n",
+    "        self.vocab_size = vocab_size\n",
+    "        self.num_hiddens = self.rnn.hidden_size\n",
+    "        # 如果RNN是双向的（之后将介绍），num_directions应该是2，否则应该是1\n",
+    "        if not self.rnn.bidirectional:\n",
+    "            self.num_directions = 1\n",
+    "            self.linear = nn.Linear(self.num_hiddens, self.vocab_size)\n",
+    "        else:\n",
+    "            self.num_directions = 2\n",
+    "            self.linear = nn.Linear(self.num_hiddens * 2, self.vocab_size)\n",
+    "    def forward(self, inputs, state):\n",
+    "        X = F.one_hot(inputs.T.long(), self.vocab_size)\n",
+    "        X = X.to(torch.float32)\n",
+    "        Y, state = self.rnn(X, state)\n",
+    "        # 全连接层首先将Y的形状改为(时间步数*批量大小,隐藏单元数)\n",
+    "        # 它的输出形状是(时间步数*批量大小,词表大小)。\n",
+    "        output = self.linear(Y.reshape((-1, Y.shape[-1])))\n",
+    "        return output, state\n",
+    "    def begin_state(self, device, batch_size=1):\n",
+    "        if not isinstance(self.rnn, nn.LSTM):\n",
+    "        # nn.GRU以张量作为隐状态\n",
+    "            return torch.zeros((self.num_directions * self.rnn.num_layers,\n",
+    "                                batch_size, self.num_hiddens),\n",
+    "                                    device=device)\n",
+    "        else:\n",
+    "        # nn.LSTM以元组作为隐状态\n",
+    "            return (torch.zeros((\n",
+    "                        self.num_directions * self.rnn.num_layers,\n",
+    "                            batch_size, self.num_hiddens), device=device),\n",
+    "                    torch.zeros((\n",
+    "                        self.num_directions * self.rnn.num_layers,\n",
+    "                            batch_size, self.num_hiddens), device=device))"
+   ],
+   "id": "858873034be01538",
+   "outputs": [],
+   "execution_count": 150
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T15:02:41.082450468Z",
+     "start_time": "2026-03-25T15:02:40.962991493Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "device = d2l.try_gpu()\n",
+    "net = RNNModel(rnn_layer, vocab_size=len(vocab))\n",
+    "net = net.to(device)\n",
+    "predict_ch8('time traveller', 10, net, vocab, device)"
+   ],
+   "id": "d59c1599998c8fd4",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'time travellerunuuuuuuuu'"
+      ]
+     },
+     "execution_count": 151,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "execution_count": 151
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2026-03-25T15:04:22.185320871Z",
+     "start_time": "2026-03-25T15:02:41.084179495Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "num_epochs, lr = 500, 1\n",
+    "train_ch8(net, train_iter, vocab, lr, num_epochs, device)"
+   ],
+   "id": "460f80bcf15ffd50",
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "困惑度 1.3, 146307.4 词元/秒 cpu\n",
+      "time travellerit would be revery erance for any hemptanef re has\n",
+      "travellery uplagstoot somethacongacout in anly fale tard ap\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "<Figure size 350x250 with 1 Axes>"
+      ],
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+   "execution_count": 152
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    "metadata": {},
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    "execution_count": null,
    "source": "",
-   "id": "3c3f71349a2e54c0"
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